speaker.
Jorge Pullin: speaker today he Jun Huang will speak about spin form on the Left shirts symbol.
Zichang Huang: Okay, so.
Zichang Huang: First, is thanks for everyone to join this seminar, and thanks for putting me the chance to do that and today's topic, as you know, it's informal issues table, and this is a work based on paper here this one it's fun and and our collaborators merging hand want you to share, you know one.
Zichang Huang: And in this in this in this presentation I have like three parts, the first part time introduce more.
Zichang Huang: say something about always and I use it, then the last part I will I will talk about how we use it to compute the information.
Zichang Huang: And so, this is the first part introduction.
Zichang Huang: Maybe this is familiar for all of you, but, but I just do some basic expression here so.
Zichang Huang: My work is on the scape scape a model and the simple model, you can consider in a simple model actually you're considering the space, time is a.
Zichang Huang: can be discreet hides there's a lot of small process and for each process, you can compute the transit amplitude for boundary stage boundary state and.
Zichang Huang: And this is something like the This is something where like the general.
Zichang Huang: passed into a formulation in the pattern your formulation you just if you want to compute search amplitude from the X X, it is state to ice final final state.
Zichang Huang: You can separate it into small pieces of the time spare time kisses and compute this each law amplitude and in the.
Zichang Huang: In Spain for model is similar you just separate the whole space a space time into smaller regions and between freedom, you have a shared boundary as well, great can be replaced by this resolution identity which is very similar to the.
Zichang Huang: formulation.
Zichang Huang: and actually this is passing this simple model, you can have a really have it in this passing population, and you can you can write down a action for that and.
Zichang Huang: I mean, as we all know that the semi classical limit on the screen for motor I can give you this quick gravity, which is ridiculous and for any.
Zichang Huang: sort of funny passing do for Malaysia actually you can it can compute observable in this way, which means that you can insert insert a function, which is co OPS horrible into the nominator and denominator, would be the parking function.
Zichang Huang: And one of the interesting observable we used in a simple model is this panels metric actually you can compute the 2.2 negative.
Zichang Huang: correlation function of his parents metric, which is the exact that and this thing actually in the semi classical image give you the private and public nature.
Zichang Huang: And I mean this is a lot of people's work before and actually in my work, and I want to compute this this 2.4 negative correlation function by a numerical work and.
Zichang Huang: We want to read, why we really want to compute it actually actually the motivation is like I want to, I want to develop a kind of awkward which has is to require this first day it's about reliability and then it's about utility.
Zichang Huang: Maybe I first seen the integrity, I want to you, I also find an algorithm that can compute up several roles in the simple model and this algorithm.
Zichang Huang: should have the following conditions, it should it should be able to go to the high speed limit, which is very important, because we always want to check the US and politics behavior of the spin for model to see if it is if it goes anything give you design limit semi classical image.
Zichang Huang: And then the thing is, I want to, I want to this algorithm adaptable multiple situations like it can calculate bossy cleon word orange and all those and.
Zichang Huang: In can adapt to different values of our company it's parameter work it doesn't depend on our state, you can use to compute for different twice it's about mistakes.
Zichang Huang: And for the existing package and simple model actually we have, what is the answer to saves for package, which was the, which was the presentation showed in the last of our project seminar but.
Zichang Huang: With actually has 222 things that that maybe maybe not suitable for task first thing is, it cannot, I mean so far, it cannot.
Abhay Vasant Ashtekar: compute the.
Zichang Huang: expectation when it stops are mostly tell me if the amplitude and then The thing is, it cannot really make the spin goes to where large here I just use the picture shown in the last seminars, you can see here is 14 spin is smaller than 100.
Zichang Huang: And then the thing is, can we really find that operation side required, and the answer is yes, we can.
Zichang Huang: In order to.
Zichang Huang: Actually order to to tell you that it really can be done so I first show you the result this result is for this picture is the result, I used my algorithm to calculate this observable.
Zichang Huang: it's actually part of the sinful nature and this picture is the.
Zichang Huang: shows the norm, of the value and this picture shows the argument of writing and you see that the yellow line actually is computed by the same as an expansion which deleting order after the expansion and blue line actually is given by the algorithm I use, and you can see that.
Zichang Huang: They in the large spin image, which means that larger than 10 to the power five spin they call them they coincide and very big way.
Zichang Huang: And the maximum speed, I can I actually used here so we're tend to the cough seven.
Zichang Huang: Also, I.
I get.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: Many notation in what does this, he with various.
Abhay Vasant Ashtekar: What is the upstairs index and downstairs index mean.
Zichang Huang: Is this supposed to be special OK OK OK so so Actually, this is a notice napalm pocket for for one for one vertex which means one force attacks and this 1234 is the number of the of the.
Zichang Huang: tetrahedron monetary hearing and this he actually is a flux operator, with respect to the to the face so here is the one to means that to the class operator.
Zichang Huang: In the face of the between the tetrahedron labeled by one, and you know they go back to Okay, so this is like for flaps operator put different phases.
Abhay Vasant Ashtekar: Okay yeah Thank you.
Zichang Huang: So this is one, this is actually one part of the same Hong Kong incorrectly it's can contains all those things but, but it is oneness report it to compute.
Abhay Vasant Ashtekar: yeah.
Zichang Huang: But in this case.
Abhay Vasant Ashtekar: Did you.
Zichang Huang: Did you but.
Abhay Vasant Ashtekar: You must use some boundaries states right.
Zichang Huang: Yes, I will say that later because no, I just wanted for.
Abhay Vasant Ashtekar: And the last question is really about is so this is all with what we call signature minus plus plus plus in that sense there's a lot of.
Stories yes.
Abhay Vasant Ashtekar: Thank you very much.
Zichang Huang: Okay, so I also compute another observable is one and another one and I if I combine that to ready, I can.
Zichang Huang: have one component of this info.
Zichang Huang: And for all this result, you can see that to be can go to where large spin and.
Zichang Huang: We really see that thing in this very large spin scheme in the very large same region actually the percentage difference between the synthetic expansion and our algorithm is quite small here in Tennessee is smaller than 10% and in the slot retains just well 2%.
Zichang Huang: And how do we really do that tactfully, how we just directly computers integral.
Zichang Huang: But they seem to have some problem generally you can call it signed problem is because the you know the information is complex reading so that this into the power minus is so cemetery.
Zichang Huang: and especially for the large speed limit the deal stage we become very severe so that if you want to compute this, this in fact expecting and where do the denominator and knowing how to search query function having unsanitary 20 months so that the value wouldn't be very small but.
Zichang Huang: But, but actually if you want to compare this expectation value the whole thing should be an old one.
Zichang Huang: And this, this is very difficult to be done in the numerical way or, more specifically, I can say that if you want to.
Zichang Huang: If you want to compute this thing's the same should give you the results for the in each of our islands or engineer or other end here.
Zichang Huang: And i'm in general, if you want to use like conventional Monte Carlo method to do this computation it will give you a variation.
Zichang Huang: In order of one over square root of and configuration is integration is the number of the samples using the money out because in long island just.
Zichang Huang: do a lot of samples and computed the name of the samples, and if you combine these two conditions together and and you want to make these things in told one.
Zichang Huang: Actually, is indicates that the end configuration, where the same often at the simple your needs to this computation would be exponentially.
Zichang Huang: To the old off in and it's actually OK, I forgot this nfl is the number of the of the wearables this actually depends on so and generally for Spain for model, this is very large.
Zichang Huang: So, it means that actually a for the conventional Monte Carlo we cannot really use it to do this or Secretary of education.
Zichang Huang: And one solution we use cases call this leaf is timbo integration and, in general, the idea is like the following so first we have this ourselves for an intimate here.
Zichang Huang: What we can do we can actually we can actually first and analytical continue continuing this all and asked to be a function of defined on the complex.
Zichang Huang: But this integral itself actually it's just this continued at interbrand integrated out at a real are in her to the core of in here.
Zichang Huang: And I mean this is similar like any complex analysis, if you want to do this if you want to do the to this empty one actually you can find another another integral cycle, which is.
Zichang Huang: which is equivalent to this so that the integral value will be the same, and then the festival method actually find one integral cycle, so that only cycle, the imaginary part of the action is a constant So if you do that integral integral psycho Sigma this this antibiotics are now for.
Zichang Huang: OK.
Zichang Huang: And then it will be possible to do this by to do this, integral by the numerical method.
Zichang Huang: So maybe I need to.
Zichang Huang: introduce this religious symbol.
Zichang Huang: So the symbol is is this, I mean you know we're at like the symbol is this, this is a piece of metal used when to sue the winners, to the.
Zichang Huang: The cultists and this one is used to push the end of the needle and actually is the similar things in this in this conceptions religious symbol so generated looks like the things is it's a manifold nailing on the critical point that's where that is.
Zichang Huang: And the more explicitly actually the religious symbol is defined as the Union of the status descent passes for into the critical point.
Zichang Huang: When he goes to infinity so in order to explain this concept actually I need to first thing to give this stupid descent equation, and this is a, this is a differential equation, and the solution of sorry.
Zichang Huang: And the solution.
Zichang Huang: And the solution of it actually I enjoy it in this way in this bring ice.
Zichang Huang: So in this in this phone lines, since it is the solution of this equation, or you can check that usually typically find that the the measuring the change of the action along this green line is purely so the imaginary part of the action is that it's a constant on this bring light.
Zichang Huang: Gray line here.
Zichang Huang: and
Zichang Huang: And you know, this is all the ordinary differential equation, so it means that it has an evolution time, it means that some point here evolve to the critical point Nice.
Zichang Huang: The definitions is that some point here you go to the critical point it's infinite time and always bring passes.
Zichang Huang: If you if you combine them together, it can make this purple mandible and this man is in this manifold as we see the sticky descent, which means that the action is decreasing with respect to the direction artists evolution, so in this.
Zichang Huang: In this purpose in this is purple manifold the action the real part of the action is large in the bottom sorry exponential E to the minus real part of the action is locked to the bottom, and it will be small in the top.
Zichang Huang: And one thing is this sacred heart more than Maybe you can ask me is this has something to do with sequel more factory is not it is just the defining equation for this particular symbol.
Zichang Huang: And then the pink elephant siri tell you that the real time actually is harmonically equivalent to the.
Zichang Huang: To the linear combination of the festivals, so I also need to explain the notation here this Sigma actually is a denotes a critical point of the action.
Zichang Huang: So for each critical point it has it simple and I cannot get us this day Sigma and then and then this series aqua guarantees that is linear combination.
Zichang Huang: Is horrifically pointing to the art, which means that I if I do this if I do the.
Zichang Huang: linear combination of the integral out if single it will equal to the today into our and this, and this, and this is called weight of the symbol is something actually a little bit hard to be calculated, but you know algorithm I don't need to calculate it.
Zichang Huang: But then the thing is, if you use the PIC ality series, you can you can rewrite this expectation, whether you into this one in.
Zichang Huang: The numerator and denominator becomes a linear combination of the integral on the sample.
Zichang Huang: And then the thing is, if there is a situation, one single dominate the integral It means that one single the integral on one single square to the larger than the into all the other symbol, I can just considering that.
Zichang Huang: I can just do the proclamation seeing that.
Zichang Huang: denominator and knowing that her become just one term just on that a dominant symbol, it will be written like this one.
Zichang Huang: And syncing the simple the mentoring part of the action it's a constant so I can call it out to be here, and then the end and this rescue face cancel, then you find that I finally got a integration.
Zichang Huang: I got the expression, where the integral and where the know anytime denominator goes now surgery integrals but the integral psychologist that.
Zichang Huang: Dominant symbol.
Abhay Vasant Ashtekar: But.
Abhay Vasant Ashtekar: To show this I mean what has to actually calculate this for all symbols.
Abhay Vasant Ashtekar: symbols and then then only then one can decide that one is dominant right.
Abhay Vasant Ashtekar: And there's not a primary reason.
Abhay Vasant Ashtekar: One is dominant or other.
Zichang Huang: Yes.
Zichang Huang: The thing is that, in the in the same form propagator actually.
Zichang Huang: We know that there is a critical point.
Zichang Huang: That will dominate the integral in the large speed limit which give you the classical geometry, and we would argue that the symbol attached to that geometry metric or critical point gives the most of the people use the same language.
Abhay Vasant Ashtekar: But how did they ask, I mean, are you saying that.
Abhay Vasant Ashtekar: That, in this particular I mean i'm not clear about this, the steepest descent, and in this lecture theory of symbols.
Abhay Vasant Ashtekar: So you're saying that because normally we don't go into complex systems all right, I mean you, you are extending into complexes so but So how do I know that in when I was done with X extension into complexes and condo complex numbers that there is only one dominant symbol.
Abhay Vasant Ashtekar: usual argument as to do the real ones right and here you're doing some extension too complex.
Abhay Vasant Ashtekar: And then there may be many other things that need I mean I think what you're doing is very exciting i'm just asking questions to clarify the status of where you are.
Abhay Vasant Ashtekar: So it seems to me that the status of where you are is that you know with this idea of the lecture stumble you are actually able to do this calculation just.
Abhay Vasant Ashtekar: Assuming that the point that we know, is the only one, even after you extend it into complexes Is that correct.
Zichang Huang: The thing is actually.
Zichang Huang: Although this is integral one thing, though, actually the most contribution part in the symbol is the integral around a critical point.
Zichang Huang: And I will say that later, but the thing is, I mean the real part I know that that critical point actually give you most the contribution of the integral.
Zichang Huang: Which means that if you want to do the whole integral without losing any upon fractions then he rose around it would be would be.
Zichang Huang: Very important and later it will see that this symbol this integral simple actually can be generated by the coins in the real crime close to the close to the critical point.
Zichang Huang: So, which means that if I if I integrate on the symbol is contains all the information of the other regions in the real climb.
Zichang Huang: neighboring, the most important point.
Abhay Vasant Ashtekar: No, I don't understand your argument, but maybe we should go on, because it seems to me that somehow, one has to establish after extension to complexes that that there is no there's no other.
Abhay Vasant Ashtekar: team building the complexes because I mean.
Abhay Vasant Ashtekar: you're doing a magic here i'd rather than deficiency some magic here.
Abhay Vasant Ashtekar: Which is that is get your the oscillator into integral to begin with, and that was reduced to something simple and that's something there's also This is something simple was done by extending to complexes and my understanding has always been that.
Abhay Vasant Ashtekar: As usual there's no free lunch.
Abhay Vasant Ashtekar: The price that you pay is really the extension to complexes and therefore.
Abhay Vasant Ashtekar: You are to really, then I mean the problem changed but still, there is a problem, namely you still have to find out all the.
Abhay Vasant Ashtekar: same symbols in the in the complexes now, whereas previously you're just dealing with real things.
Abhay Vasant Ashtekar: And I am I am happy with you just to say well let's just do this and then we'll worry about other points, but I don't understand the argument, saying that.
Abhay Vasant Ashtekar: That they must be obvious dominated by the critical point which really came from the realtor but, but we can go on, and then we can play explain later.
Zichang Huang: Okay, so yeah one thing is actually the one single dominant indigo is not really a common situation, but it is the situation happens for the sinful nature which even hungry state, and I will say that.
Zichang Huang: And then the same is.
Zichang Huang: The symbol of OK, so the same than the simple actually if you if you reveal that definition Assembly to actually not really easy to be find.
Zichang Huang: Even you may not be quite it's not really even you need to be fined by the computer so actually we have to do some approximation.
Zichang Huang: The first thing is actually the symbol is is the is the Union of the past 14 to the critical point but it's a little bit hard to find find the past exactly pointing to the critical point what we do is we we we first considering.
Zichang Huang: The situation, the unity of the past 14 to region close close to the point, like this, when disk here and the screen, this is an real dimensional manifold or a neighborhood around the critical point and.
Zichang Huang: If I if I do the Union for the past it's pointing to this screen printing this it will generate this Green manifold outside it's purple manifold.
And we know that.
Carlo Rovelli: that's a clarification question sorry.
Zichang Huang: Just a.
Carlo Rovelli: symbol itself goes into the complex better is the critical point, still on the real or is somewhere in the country.
Okay.
Zichang Huang: The decoding are the critical point of the action before the analytical analytical continuation is on the reply, but there will be more critical point after you to the continuation.
Zichang Huang: Okay, but, but then The thing is, I mean like in the case that the geometric pretty good point is really out.
Carlo Rovelli: Of the okay.
Abhay Vasant Ashtekar: But that was essentially my I mean not essential that was part of my question really because typically you do get critical points outside and you get many symbols also.
Abhay Vasant Ashtekar: And then, and the question is well how do we know that those are neglected, but I mean it's not surprising right because, as I said before, I mean.
Abhay Vasant Ashtekar: What is really converting oscillator integral to something that can one can calculate so.
Abhay Vasant Ashtekar: It looks like magic and there's always a price to play it right, the price to pay is additional things potentially contributing, but then some cases it doesn't they don't contribute and that's what he's looking at yeah.
Zichang Huang: yeah yes that's really the situation that's released this situation, but I will say the details of all it's been talking about later later bye we can flag.
Zichang Huang: Other points okay and but but for for that critical point actually what we can do is to do the automation and the first.
Zichang Huang: The first step of automation is getting the screen one screen wise down by evolving this done by the okay somebody passes the Union of the passage pointing to this when this clear.
Zichang Huang: And then the thing is still a little bit hard, because I mean, as I said, the screen one is the past 14 to that if you really use a computer, you should pop up early know that, where is the.
Zichang Huang: Where is the point can pointing to the so in this we Sigma but then the thing is actually I can I can use open site flow, which is as a flow if you say here.
Zichang Huang: I don't I don't have this model sign ssd for, and then I can I can, I can say that I just need to do a approximation, as this as this one, this red one is the.
Zichang Huang: Is the point is made by the points on this Green desk we Sigma after all, is a flow for our final time just come to this red one.
Zichang Huang: The thing is, if this we segment small enough, then this red one would be you would be a good approximation, a part of the green one and be a good engineer good approximation of the part of the purple one.
Zichang Huang: Part means that it only contains the part close to the critical point.
Zichang Huang: But then the thing is, we know that if we do the integral we have this wait this way to actually decay is very fast waves go away from the critical point, which means that if you do the integral, the only contribution part would be just this red heart close to the critical point.
Zichang Huang: And then I use it use this one as my approximated symbol to do the computation.
Zichang Huang: And then the thing is, I said that I need to have a we Sigma the screen desk to to use it to generate is rack symbol.
Zichang Huang: The thing is a which which n dimensional manifold close to a critical point would be good to to jump to be a candidate of we Sigma the same, and then we can do mean that needed the neighborhood of the previous point to see what happens is as a flow and the.
Zichang Huang: The.
Zichang Huang: Poverty of the act as a flow actually given by this equation by this general adding value equation is he is the half of the action at this point.
Zichang Huang: And the census is already accomplished slide is already a contest number value so actually actually I can equation becomes a little bit different.
Zichang Huang: bar here, and because of the because of the leftist electric siri actually, we know that for each critical point actually I wouldn't have like.
Zichang Huang: To if it is a n dimensional dimensional manifold I wouldn't have to end lameness and half of them would be positive and half of them inactive the indicates like a.
Zichang Huang: Like to the end directions like this spring one.
Zichang Huang: which was where, if you if you put your initial point on the screen directions, the as a flow the flow this point of way to generate is this red symbol 20 if you put your initial point in this purple directions which is Director has an active where they asked.
Zichang Huang: The SA float.
Carlo Rovelli: just push it to the critical point.
Zichang Huang: And since critical points a fixed point of the essay floors or it will keep it there, well, which means that if you want to have a very efficient computation we seek my can choose is.
Zichang Huang: Is the subspace expand by the vectors that by the atom letters which has quality evacuated, which means by the screen actors, so we see we see my views they can be expressed in this way.
Okay.
Zichang Huang: And then the thing is, if I do the flow actually the the volume element would be different from using much showcasing so I mean.
Zichang Huang: You can use this picture as an example, this picture shows how a volume indicated by this cubic will change with respect to the flow, this is proof law.
Zichang Huang: And more explicitly we can calculate it so The thing is, in the you know that we use we have this this expression actually I can use acts as my coordinating we see one and then.
Abhay Vasant Ashtekar: The last question, what are the last ones place up I just say this, he really did the Haitian and therefore this complex right.
Zichang Huang: You know and.
Abhay Vasant Ashtekar: But you're saying that I get values are guaranteed to be positive, or are you just focusing on positive I get.
All.
Zichang Huang: The.
Zichang Huang: pika pika licious siri guarantees that the eigenvalues should have two types one hype would be the positive rewind one would be negative.
Zichang Huang: ice and they will have the same number.
Zichang Huang: of positive.
Zichang Huang: that's counted by the pickle efficiency.
Zichang Huang: Okay, yes, we will give you know some and focusing, and then the thing is systems we use access the coordinating we Sigma so actually.
Zichang Huang: We can compute to the Dakota Kobe on this we seek month, which would be determined trade estate each line of the day, you consider the the expression of the Omega, which is the base letters.
Zichang Huang: And then, and then we can use linear right as a flow to describe how a vector can be can be can be can be both with respect to the flow so.
Zichang Huang: The linear right as a flow will be this equation, and if you solve this equation, you know that how a vector J K from here would be evolved to Jay activity and he.
Zichang Huang: is a symbol so so, then I actually can write the volume element in the symbol, as the as the determinant of this katie you, they have to.
Zichang Huang: And then the thing is, if I know what's the one element in the symbol, I can write the integral on single as an integral on the wiki Sigma which contains the jacoby.
Zichang Huang: And then, if I put this relation into our equation here our competition and we find that the post post Dino entire nominator will be the integral on the we Sigma.
Zichang Huang: And in and then The thing is, I can do some I can do some.
Zichang Huang: rearrangement of the number first thing is, we know that this determine Jay will be a complex number and then another thing is the imaginary part of the action on this approximated singleton would not be a constant into it, since we have a we we have a we here so.
Zichang Huang: But since we is very small us.
Zichang Huang: Then the also also a solution on the single would be somehow very moderate, so that it won't affect the accuracy of the calculation so The thing is, I can I can considering the.
Zichang Huang: I can, considering the following way, so I first arrange the real part of the action and the real part of the law to determine, it should happen.
Zichang Huang: To be the effective action and then I combine the the angle, the argument of to determine after the Caribbean, and then a metric part of the action combine them together as the rest of your face, and then I define the kind of.
Zichang Huang: expected value effective effective effective expected your wedding was this way where the action in the partition function ucsd effective back then I can write this expectation of F into this things where the denominator, the the.
Zichang Huang: The the rest of the explanation of the rest of your face times the APP and nominate.
Zichang Huang: nominate for wouldn't be the rest of face when when they have the rest of PICs and they're saying actually supposed to the denominator can be computed by the by the Monte Carlo method.
Zichang Huang: And the thing is, you can considering this effective action you to the power of minus effective action as a postman factor and then just do this, you try try to find the symbols on the.
Zichang Huang: wii Sigma following this bozeman factor and then compute the meanwhile the office rescue face times F among the same amount of samples who kept and compute the memory of the rest of the face amount same simple, you can put it in the denominator nominate finish your competition.
Abhay Vasant Ashtekar: How do you control the errors.
Abhay Vasant Ashtekar: Because when you replace everything by the effective.
Abhay Vasant Ashtekar: Presumably that approximations and so is there.
Abhay Vasant Ashtekar: Is there any control on these errors that you are making in this in this description.
Zichang Huang: Ah, so actually.
Zichang Huang: There are there are something here, so one thing is I don't want to the vibration, of the imaginary part of the action to be very large so.
Zichang Huang: So, so that so that to make this don't know me I know mentor to be verified your territory and this thing can be controlled by choosing a.
Zichang Huang: Small side of me so actually one thing I can do is I took I give a are bound limit of this we Sigma or the largest volume of this week, so if you control the side of me then to be slower than the magic part of very sharp the metric part of the action would be small, so that the.
Zichang Huang: The integral the oscillation of the integration would be small, and then the.
Zichang Huang: The arrow will be slow for the whole computation.
Abhay Vasant Ashtekar: Okay, but there is no quantitative estimate yeah so I mean I think what you're doing is very beautiful i'm just trying to and this.
Zichang Huang: is another thing is just the just the standard.
Zichang Huang: error control for for the for the Monte Carlo method, it depends on the number of a simple to get I mean is, is quite quite the standard is.
Zichang Huang: The the arrow should be older of square root of one divided by the number of simple us so, then the thing it depends on how many samples you get in the Sigma and it's just a quite standard arrow estimation for for the month so.
Abhay Vasant Ashtekar: Okay.
Zichang Huang: Okay, and then the other thing is, I mean the denominator, I know, it can be computed by the Monte Carlo method.
Zichang Huang: Actually, not to really conventional hello, so this mark of payment method and this method actually can generate samples following following given any given distributions like this was my factor.
Zichang Huang: And then the thing is our in our situation for the actual action actually has a lot of variables so so so here in order to deal with this.
Zichang Huang: High dimensional Monte Carlo method actually I use one specific metric the method called dream which is differential evolution adaptive metro is always on.
Zichang Huang: This algorithm it has a very decent wearing a lot of details but, but here, since it's not really important for our discussion I just say that advantage of it so actually it gives you a very high efficiency, because.
Zichang Huang: It can end for the Monte Carlo method for a simple, you would accept or not accept it as it as a simple following the certain distribution.
Zichang Huang: But this this thing actually give you a good acceptance rate and a very fast speed, so that so that's the simple procedure can scan the whole.
Zichang Huang: The whole region, which is important for integral very fast.
Zichang Huang: And then it actually adapt to the Multi modal distribution the Multi modal distribution is something like this one here, you can see that it has this distribution has to pick up tickets at 10 the other tickets at minus 10.
Zichang Huang: And if you use the conventional metropolis mastered it generally just starting one it was stuck in one distribution peak, but if you use this cream.
Zichang Huang: cream algorithm me to use multiple chains to to do the sampling, so it actually can and few this peak also and, as I said, because this screen or, it also has wanted you're seeing in scanning different regions of the temporary.
Zichang Huang: manifold simultaneously because he use multiple chains and they also it also adapt to the particular computer processor, so it gives me a very high, it gives a very high efficiency to do that computation.
Zichang Huang: And then let's go to the swimming pool heater so that means that, I mean I said a lot about about the lifter symbol and and something about the algorithm The thing is, if it can be really adapt to the same phone call it her, and here I have this example.
Zichang Huang: So, then, the thing is.
Zichang Huang: I mean spam folder have will have many types and what we used in the Community in this example is the PR spin for model and it's quite standard here so.
Zichang Huang: They spent from amplitude can be reading this way and the doorway state we use is a coherent bounded state which has a which it is a linear combination of different spin spin networks and that the commit the weight or the way packet is right me in this side here and for.
Zichang Huang: For the each for each amplitude after face to face amplitude I could insert a white map which maps the.
Zichang Huang: which might have to spin Jay massey 20 which is perfect patient to that out to see us for the station and embedded a.
Zichang Huang: very nice for me to come here and in our competition we choose ghana's point one.
Zichang Huang: And then actually that.
Zichang Huang: For some tax amplitude can be writing in this interval in this passing to form.
Zichang Huang: The action you can actually at least writing this way is is what we use very standard and but the thing is in action, there are several parameters depends on the boundary state.
Zichang Huang: Which is this casino, which gives you the three dimensional normal of interfaces is precisely this this way packet in our state, and this data is one time between this site and J is the somehow consider it does the real the area of each faces.
Zichang Huang: And to to define the boundaries state has first I need to define this net parameters and then the thing is.
Zichang Huang: This is what we really do is we, we find that we we use a channel we use a boundary State has a Joe Joe metric interpretation and which means that it has a correlation to a full sentence so so this force impacts actually given by N minus data so here, I have the.
Zichang Huang: coordinator of the forward has itself the force attacks like P one P two P three and with this coordinates I can compute and the area of of the phases.
Zichang Huang: In this table is just some area of five some area to call him, Sir, this 12345 MINS the the label of each each side, they will eat like 12345 and then ap means is the faces.
Zichang Huang: faces from one to 10 one, two or two from terrorism, what and then they have they have areas like five and two if you if you have a.
Zichang Huang: Bird has is coordinating this way and with this quiet, we can also compute the fourth dimensional no i'm sorry three dimensional normal food faces in this way.
Zichang Huang: And then we can compute and the for them if normal of each of each tetrahedron in this way is hosting service classical geometry offer for setbacks and we want to find a boundary state, corresponding to this is classical geometry, so it can be writing this way.
Zichang Huang: So, as I said, this coherent boundary state is a company or combination of different networks, this spin up this entry entry is already in the in the last.
Zichang Huang: table, and it will give you the whether you have the senior and then another thing is is the volume so we've hackett.
Zichang Huang: In this way, packet you have like two different parameters, why is this data wife is arpa this data actually values in this table the way we have nita I use it in this table it actually relates to the.
Zichang Huang: To the to the database, a lot of different for that country normal and I will say that later and then another one is this arfa.
Zichang Huang: This arm, I need to specifically say that so actually this arfa it's not really it really randomly choose in the discussion actually.
Zichang Huang: You should come here the mean if you have this arfa you can compute it, you can compute the applicator but then The thing is, you can compute that you can compare your computer results with like ridiculous or other brevity siri to really to really to really find a proper are.
Zichang Huang: But then the thing is, I mean in my work what I really focuses is about whole if my algorithm really works, so the idea is that if I randomly choose arfa and.
Zichang Huang: And I use this harper and I use this arfa to do my computation and I took my computation with respect to the little symbol, and I also use this arfa to do the computation.
Zichang Huang: With respect to the same topic expansion and then The thing is, if I come on compare the festival result endings central expansion result if I find them fine.
Zichang Huang: I found and like they can match, then the thing is that my hours of work.
Zichang Huang: So so actually in my work, I really randomly choose the art.
Zichang Huang: And then the thing is, if the algorithm work for random trust it should works for the right heart, but it can give you the propagating.
Zichang Huang: So so actually you may be different, is when you choose.
Zichang Huang: And then the thing is after I have been very active, the boundary and also fine, I also have a critical point which give you the full sentence geometry.
Zichang Huang: here's a critical point means the value of key and well you obviously the GMT already seen in in the in the in the action, and this this this value of G and D actually tell you that how this tetrahedron can be embedded into the space time so that they can grow together today for syntax.
Zichang Huang: and generate and mean if you really could back this lady off gnc in the critical point Krishna find that they are the solution page, but one thing wasn't here it's about this this data here.
Zichang Huang: Because I mean the I mean the action.
Zichang Huang: In action in the palm of his action in the sniffle or using if you use the coherent Bobby States actually generally you will you will combine this precise into the action to be an action, action total and what you require is the.
Zichang Huang: Partial derivative of Jay with respect to play with respect to this total action can give you do so, so here actually the details choosing the way that.
Zichang Huang: The derivative of Jay with respect to the origin, no action will give you this this data and then you put into a problem back to the definition of as total.
Abhay Vasant Ashtekar: So hundred dimensional integral are you doing here I mean.
Abhay Vasant Ashtekar: In terms of seeing that you explain to us, they know that was an RN and then you got to see and so now, what is the capital in here for the audience that you start with.
Zichang Huang: Is 45 real dimension for what you find real real parameters to.
Zichang Huang: run that action.
Abhay Vasant Ashtekar: But okay.
Thank you.
Zichang Huang: Okay, and then after action when we need this is holly really right it's this this problem later it actually contains two parts, the first part has four.
Zichang Huang: FLEX operator, and the second markets so multiplication up off the expected value of two classes.
Zichang Huang: And this proxies can be inside inserting into the into the action is way, so it actually a half long tough.
Zichang Huang: Is amplitude from face to face, and if you insert a flux operator in here, it will give you this terminal and if you insert a flux operating in this in this fix this fix it will give you a minus sign and then and a little bit different expression here.
Zichang Huang: What was.
Zichang Huang: The last question.
Zichang Huang: What did I say I said 45 or 50.
Abhay Vasant Ashtekar: Yes.
Abhay Vasant Ashtekar: What if I.
Zichang Huang: am sorry it's.
Abhay Vasant Ashtekar: A super high.
Abhay Vasant Ashtekar: Okay okay.
Abhay Vasant Ashtekar: Fine yeah Thank you.
Zichang Huang: it's a little bit later so maybe I.
Abhay Vasant Ashtekar: Should should.
Zichang Huang: Exactly okay.
Zichang Huang: So so actually if you insert the flux home printer in your here, it will give you a little bit different result not not really so surprised you'd have to have a bias.
Zichang Huang: And then the say is I can express it the expectation weddings of the things in this way, so this is defined this just just an inspector view.
Zichang Huang: And then, but, but this thing you cannot directly use the method and just mentioned, because.
Zichang Huang: I mean you have an integral over over or holder or the other parameters here I use this this fight, just as just indicating the parameters, with respect to Z and Z.
Zichang Huang: And, but but for for the for the variable J us, you have you have a summation instead of being, but what we, but the you know our algorithm I should have an indie rock all the variables, so I still need to do some some operation on these things.
Zichang Huang: So actually what I use is possible information, the problem is, I make sure I can change the summation of.
Zichang Huang: All of the heart integers and zero to be a summation of the intervals of a lot of continue continue integrals in this way.
Zichang Huang: Which means that my into my into my actually can you write an essay some a lot of integrals with this for hi Kate here.
Zichang Huang: And for this submission actually the first thing I can I can I can I can neglect is this APP zero turn So if I.
Zichang Huang: If I remind this precise actually can be writing this way.
Zichang Huang: And this thing affiliates address a gaussian distribution, which means that, in the large London limit the most of the distribution comes from the point of the day that close to zero and.
Zichang Huang: Another host to yet for this one is close to do but Lambda is directly it's very large farm farm farm farm farm absolutely i'm so angry that they will turn can be neglected.
Zichang Huang: And the evil I laughed at the academic term I still have a lot of some agents here and then The thing is, we know that in the large.
Zichang Huang: interlocking in the large take his are swimming case actually what really contributes to the to the to the integral St is the critical point.
Zichang Huang: One thing is for for the for the high choose the only critical points can happens when he goes to do so.
Zichang Huang: So, only one case because to do this as photo of US total has a critical point, which means that for for for the term that came that doesn't equal to zero.
Zichang Huang: it's not really it comes and it continues, only a small part.
Zichang Huang: So when you.
Zichang Huang: When you have a term that kayden.
Zichang Huang: Yes, and this is what I really right, it was interesting that it says that only the critical point during the whole integral and for the tightest choose only the K equals, to the return has a critical point, which means that I neglected to take not equal to zero.
Zichang Huang: and actually I can write all these things into into box, but here I clean neglect one steps, so I mean in one page before it is zero here, but here in this page I have minus infinity.
Zichang Huang: But the reason actually is it similar to to the reason I blacked at blue.
Zichang Huang: And the thing is because of because of the as total has a has a gaussian distribution this fake so when when the when the day is when the long legs very large the part of the integral far far far away from the Lambda play it's not really important, so I can actually I can actually.
Zichang Huang: add the the minus at the integral from minus infinity do to this to this angel.
Zichang Huang: And then the city and then this form, is something we can apply our object, it has the integral of all the wearables and action is correct, well, it action.
Zichang Huang: And then yeah and then The thing is, and then, finally, to a small summary of what I have, I have a action depends on wearables and this accents come back sweating and with this action, I want to compute this three.
Zichang Huang: These three things and combine this racing we can have that propagator.
Zichang Huang: And then the thing is, I mean if I use my algorithm what really what really happened was that.
Zichang Huang: The thing is, as as probably as you realize that if you do that analytical continuation, you will have more critical points than just the original action and, yes, and then, and then the thing is.
Zichang Huang: We can know that this newly created critical points is potentially suppressed.
Zichang Huang: At the large speed thing.
Zichang Huang: And the other thing is another thing is that we actually compute this after will only on the on the on the symbol that attached to the dominant critical point and, in this situation is to the is the simple attached to the critical point corresponds to the four simple at scale.
Zichang Huang: And this competition actually actually contains all the conservative corrections, which means that the correct department corrections eligible for around the geometric critical points, and when you lacked non productive.
Zichang Huang: Long did it correctly corrections which is exponentially suppressed in the large spin situation and what we really, and here I just do a summary of what we're really black.
Zichang Huang: Bear can elect the art and the sub dominant symbols were actually neglect the case doesn't equal to their own terms and neglect and the.
Zichang Huang: absolute terms in the in the Court on reservations know we also neglect the integral from minus infinity to zero, because in the large spending this thing doesn't really contributes a lot to the to the people.
Abhay Vasant Ashtekar: Come back to your second second point in the last month, but it's yeah that I mean.
Abhay Vasant Ashtekar: Where does that come from that that action is exposure surprise because the right situation and cosmology when this is not happening, and in fact the extra.
Zichang Huang: Yes.
Abhay Vasant Ashtekar: New boss actually are critical to the final result, so what, why is it that the yeah.
Abhay Vasant Ashtekar: What is it about the spin form that says that the critical points the additional critical points and complexes suppressed.
Zichang Huang: Okay awesome so The thing is, I mean in general case for the same form, this is not happened, but for the smartphone later.
Zichang Huang: I mean from the previous result, we know that if you do the analytical continuation, we know that the only contribution critical point it's a.
Zichang Huang: it's a it's a geometric way of pointing the opposite force attacks and and and which means that the common correction should be given by a kill my day.
Zichang Huang: The content that the dominant on the corrections was given by the points here the geometry.
Zichang Huang: And that's that's the trick with us here, we just think that.
Abhay Vasant Ashtekar: So Are you familiar with it, what happens and kind of cosmology when people found that things that were done by hockey hockey and so on.
Abhay Vasant Ashtekar: were more or less living in this the real section, but then you know, there are parts in the complexes which are actually very important, so they are also I could I met qualitatively same argument that there's the real one there's only one critical point, and so on, but.
Abhay Vasant Ashtekar: yeah that that turned out to not to be correct, so what is the difference conceptually yeah.
Zichang Huang: I mean.
Zichang Huang: Okay, so so this thing here is because we actually I mean previously, we know that a lot of the propagator it just given, I mean it.
Zichang Huang: is indeed.
Zichang Huang: The reasonable, the reason but result it's given by the the geometry point I mean for the for the algorithm I just said here, it only works for for the situation that you have one dominant symbol and but but but But there is another there is another.
Zichang Huang: Modification of this of that originated can adapt to the situation and have.
Zichang Huang: That may contain all the contributions of other symbols, it is unbroken now.
Abhay Vasant Ashtekar: is the next step okay.
Zichang Huang: Okay, and I really agree with your point that we don't already know if there are if the newly newly appeared critical points will contributes to the results were other frequently contributes to resolve.
Zichang Huang: That can be neglectful I mean I mean apparently we don't know, but for the situation propagator we actually first of all, definitely be there, so.
Abhay Vasant Ashtekar: Okay, so see I can subscribe to extend it so are you saying this because there is an agreement that large J where you know that analytical results, or is there, something which was.
Abhay Vasant Ashtekar: Is that the main argument that you have in mind that, because it agrees with what the analytical results for large J, therefore, these things should be negligible rather than a priori argument which says that these things should be negligible.
Zichang Huang: I mean for for this situation, yes I think my argument based on that claim.
Abhay Vasant Ashtekar: Okay, thank you.
Muxin Han: Well, actually, if you if you go through the peak of little siri.
Muxin Han: You can also be that.
Muxin Han: You can also prove this, this second statement, and if you get additional complex critical points they only contribute.
Muxin Han: Now suppose they contribute and they only contribute exponentially small.
Abhay Vasant Ashtekar: No, I don't think we should know about this.
Muxin Han: Yet the other example you you you, you mentioned this huddle what they are doing is the Euclidean possible with e to the minus action and actually it's real and in that case, yes, you have complex sentences and complex hadn't made on it, but, but here it is the oxidative rates, the nature.
Muxin Han: So that's the difference.
Muxin Han: The real.
Abhay Vasant Ashtekar: Good good good so you're saying that if in fact there's also military behavior then picker lipstick does tell you that completely generally the extra critical points that you get would their contribution will be exponentially surprise is that something in the picture little scary.
Muxin Han: Yes, I think.
Muxin Han: Yes, I think it's not hard to see because of.
Muxin Han: Probably we can do that later, but if you if you look at the definition of leeches symbol and suppose you have an intersection between nuclear symbol and your integration.
Muxin Han: Access your real axis, then what these because the symbol is amuse generated by don workflow so, then the value the real part of the action is much must be smaller than the bedroom at the very relaxing.
Muxin Han: So okay.
Abhay Vasant Ashtekar: And that was not applied the greeting signature somehow because.
The I.
Muxin Han: guess I suspect.
Abhay Vasant Ashtekar: Okay, thank you very much, wishing for interjecting because i've been confused about this, thank you.
Hal Haggard: Have a question related to this as well, so I mean doesn't depend on the parameters of the model to motion, that is, we could have critical points that are only.
Hal Haggard: That are off the real axis, but you know, as I tune a model parameter they might come closer to the real axis and become more relevant.
Muxin Han: that's right and it's all I mean there are lots of there can be stocks right.
Muxin Han: Right.
Muxin Han: yeah they can be but So yes.
Hal Haggard: So in principle the second claim also depends on the barbero parameter for example.
Muxin Han: Oh that's right that's right So yes, so I mean we are not complex by the by very nice parameter so so we just take a real number fix that real time.
Thank you.
yeah.
Zichang Huang: Okay, so.
Zichang Huang: Is there any other questions No then our company.
Zichang Huang: And then the thing is for for for the for both the numerical Sir sober of the essay equations and cream optimizations.
Zichang Huang: dream operates and actually I have several optimizations for that, but this is just a technical details, you can find it in my paper.
Zichang Huang: But I think what people most interest will be on this result so here, although I already showed you this regard but here I just sent and more clearly, so one thing is.
Zichang Huang: Whether you can find is that I mean from the difference percentage difference actually what you can find it is.
Zichang Huang: really is like, if you land a greater than 10 to the minus five for these types of the expectation, where they use the personal differences even smaller than.
Zichang Huang: More than 1% is just.
Zichang Huang: Point something percent.
Zichang Huang: And, and then the in the Lambda like what how read it has 8% person, the difference so assign me claim that if you want to find large speed limit for this calculation, it should be greater than tend to.
Zichang Huang: tend to the car five.
Zichang Huang: and similar things happens in this type of expected values if you have to flux operators, it also I mean it can be somehow somehow if you if you compare it if you really look at the situation in the 10 to the minus the potential power for is still like smaller than 1% difference and.
Zichang Huang: And here are those see that these two lines or the almost coincide, but this is because, because this is a logarithm.
Zichang Huang: Actually test several difference, especially in 100 and, if you look at the the the the argument, the angle of the expanded the complex numbers, you find more obvious difference, then.
Zichang Huang: As similar things happens in this in this expected to me.
Zichang Huang: And then the saints is here.
Zichang Huang: Okay, so so for the propagator in actually just combine the previous two resulting.
Zichang Huang: propagator but what you can really see is that percentage difference.
Zichang Huang: Even though for for the spin greater than 10 or five it is larger than than the previous three results as any it's because actually is a pollinator sorry.
Zichang Huang: it's complicated.
Zichang Huang: Actually, actually is.
Zichang Huang: Actually.
Carlo Rovelli: Sorry, I have to leave at something to do, I just want to say i'm sorry and congratulate is is very impressive work so and.
Carlo Rovelli: So, thank you very much and thankfully now.
Ah.
Zichang Huang: OK so so this large percentage difference.
Zichang Huang: Because i'm using a desktop it other I just camera.
Zichang Huang: Because it's because it's given by this, because this things because it is like my expectation wedding minus another.
Zichang Huang: To inspection went at the multiplication opportunity expected wedding sort of actually the the Horn, the corrections or is off high old is Kim at higher order.
Zichang Huang: So, although in the previous in the previous calculation, it has small difference personally difference, but here is because the correction came about high order so so with the same data integrity give it a larger percentage difference here.
Zichang Huang: And then, the situation is for the perpetrator i'm in the mortgage or it has like a lot of indexes and you can you can choose numbers actually it has a lot, it means that it has a lot of components.
Zichang Huang: If you counted in find that it has 1275 components and one advantages of our algorithm is that we don't need to.
Zichang Huang: redo the sampling procedures we don't need to redo the metropolis method for cloud computing all these components can just use same side of the same course to do the computing have different.
Zichang Huang: Different expectation weddings I mean each components, you can complete can consider it as a different expected awareness of the obstacles and then The thing is, are these all these components compatible with the expansion and then check that so I showed it in these two pictures.
Zichang Huang: The first picture comes from the data in London, he goes to 10 to the power of six, and this this picture is a histogram.
Zichang Huang: off the difference between the between the metropolis method and central expansions and you find that most of the components, this is, I, if I remember right is 1140 couple.
Zichang Huang: Has the present different smaller than 10%.
Zichang Huang: And they're about some some small this one, only one component that has a very large sample large influence over them already, but this is because this is caused by the fact that I don't have enough simply and, if I have enough cycling there, there will be attend a tendency that the.
Zichang Huang: The percentage difference of this component would actually go back to this to this smaller smaller.
Zichang Huang: And the situation intend to the power of seven would be quite good, you can see that the most the largest inferences it's just around the 40% and most of them is smaller than.
Zichang Huang: 5% This too is the ground, based on the same number of the same of the samples, and it shows that in the longer it goes to tend to the core of seven actually the first older a central expansion.
Zichang Huang: domains more of the table.
Zichang Huang: Yes, actually that's that's all the result, and then I will say something about.
Zichang Huang: The science of how we can use that to.
simone: Johnny Can I also ask a question not before the end because they also, unfortunately, have a cut off.
simone: These definitions here we're still seeing in the previous slide that then based grammar.
Zichang Huang: Reviews right.
simone: Here, I just wanted to understand.
simone: How much can you distinguish you know, like the result, about the fact that the syntax is not being.
simone: reached reach the exactly from errors in the in the numerical approximations you're making.
simone: I mean i'm asking, because in in simpler systems like.
simone: 3D bones energy or the Berkeley model, the metrics we didn't need to push this beans so high, in order to use some.
simone: Some expected a synthetics but here it seems that, even with beans very, very high you still have some are you happy with, I mean i'm just trying to understand.
Zichang Huang: Are you.
simone: Are you, seeing that.
simone: We really need to push to those high speeds in order to recover the expected leading orders or there is some effects here which have to do with an American approximations you're making and which they seem to be smaller for larger speeds that's what I mean.
Zichang Huang: So.
Zichang Huang: So one one thing I me I didn't try to reach him Hello modal so so I not really i'm not really know the poverty of that that model really shows that, where is the screen, where is the high speed limit.
Zichang Huang: And, and another thing is, I mean.
Zichang Huang: If I get it right, the the previous calculation is based on the amplitude and this one actually based on the expectation weddings so so actually I don't expect that they happen, I mean they're large speed limit would be the same, I don't I don't expect that because I mean.
simone: For the gravitas propagator you.
simone: We did numeric some degree we don't.
simone: learn more.
Zichang Huang: about that, but, but the thing is it's not really a big orange and all the data that we are different.
simone: So okay.
simone: Okay, so you're saying so you're saying that.
simone: Even though we let's say Bobby Clinton and Barack remodel spins of let's say 30 were enough to see the fall off of the propagator because it's a wrench any Pirelli may be so much more complicated, then you have to increase of many orders of magnitude before you see this.
Zichang Huang: yeah I see what we got here is just based on the calculation, based on my calculation it's indicates that I mean in this range of the spin it give you this person, the difference between the first order expansion to action on the computation and.
Zichang Huang: I mean.
Abhay Vasant Ashtekar: Unfortunately, similar left so.
Abhay Vasant Ashtekar: Okay yeah this is this but, but the do you mean I mean this to me also, this is a critical question really was previously it look like you know, maybe just jquery 2030 was enough to do everything.
Abhay Vasant Ashtekar: So could you go to Euclidean model and check there, I mean the click case that other people had looked at and and you use your Meta.
Zichang Huang: same approximations.
Abhay Vasant Ashtekar: And then you will get I mean, so it will be good to check if in fact you in those cases, you also find good agreement when Jay could Lambda 20 or 30.
Abhay Vasant Ashtekar: Is that is that.
Zichang Huang: yeah that's something definitely we can do, and the current work only happening, this is EPI Amato computation and.
Abhay Vasant Ashtekar: Just to sort of get.
Abhay Vasant Ashtekar: A feeling, because I think psychologically for many researchers, this is an important issue and also, I think, sums up with conceptually.
Abhay Vasant Ashtekar: Whether one has to go to this large space to get this I mean by large is still quite small because you know competitive landscape say yes, but, but you have to go to tend to 627 of value of Lambda or do it is enough to get go just to 20 or 30 I think that is a.
Abhay Vasant Ashtekar: cycle, yes, actually, I think this is really important to for us to understand.
Zichang Huang: Yes, I agree with that actually actually I mean we may we may attack it in the future.
Abhay Vasant Ashtekar: To see yeah I mean what.
Abhay Vasant Ashtekar: Does then so that this thing that she was raising that that she would be you know about whether you need to go to this large thing because of various approximations you made the process or whether it is yeah, so I think that would be good to check Thank you.
Muxin Han: Just one common I think what simoni days.
Muxin Han: He left, so what they say they find that even at small skin the pan, some agreement, I think the agreement agreement is like the order of magnitude.
Muxin Han: it's not the precise number agreement, but here, you can see that chief halton middle at tend to the to add at 100 the different is 30% so, which means he already and is indeed the at Lambda equals 100 K equals 100 they fund we've been agreement at same order of magnitude.
Muxin Han: So I see that.
Muxin Han: This is what they say agreement is they are just a order magnitude magnitude so in Defense here, we also have an agreement that small screen.
Abhay Vasant Ashtekar: yeah it's too bad that Somalian not here anymore, that would it already like to clarify this, because I think if we did if they did a case that.
Muxin Han: yeah.
Abhay Vasant Ashtekar: yeah what what what the two of you are saying that in fact you do need to go to large enough thing, maybe I guess you know jquery tend to the seven is not very large you know, compared to the because you have multiplied by 10 squared.
Abhay Vasant Ashtekar: Which is very smart.
Abhay Vasant Ashtekar: But I think that's good to know that that thing Okay, thank you, thank you.
Zichang Huang: Okay, so so then we continue just say the future plans, one thing is, we can I mean here I just computed The co hitter for a one same one for some time actually.
Zichang Huang: We can we can try to compute this info together a more complicated case, maybe we can use like a mobile one 500 is just contains more vertices.
Zichang Huang: And then we can also use the method, I mean this message doesn't isn't confined to compute the expectation after slash operator actually compute other operators, maybe.
Zichang Huang: Like you can define the operators and then maybe see what happens in the flat brightness problem, and also, we can try to improve the efficiency of the algorithm.
Zichang Huang: For for the money how apart, maybe you can apply more advanced the monocle method and then another thing is.
Zichang Huang: Actually, this St flow and metro region if you combine this St flow and the metroplex operator, it is possible to find the critical point if you I mean if you don't have it already know it, because if you see that.
Zichang Huang: For for the situation that we we do the same quality, the most possible point to be simple, is actually just the critical point, then, the thing is a.
Zichang Huang: Then the same as if you just randomly randomly do the same thing, I mean Finally, if you count which point has to be at which point it is simple for for for the most times, it may be very close to the critical point, and then there is somehow indicate that we can try to use it to find.
Zichang Huang: And this is a reference hope for all the things.
is finished.
Jorge Pullin: questions.
Jonathan Engle: I have a question about your approximated symbol.
Jonathan Engle: You.
Jonathan Engle: Part of your approximation of the symbol is.
Jonathan Engle: In order to get some sort of control over the error, at least make sure it's it's a reasonably small you make the the approximate symbol small enough and you're assuming that the dominant contribution is going to be from the critical point is that right.
Zichang Huang: Let me just go back to the next slide.
Zichang Huang: One one thing is for this approximation, the first thing I have like to place to do the to do the control, the first thing is the size of wheat.
Jonathan Engle: yeah.
Zichang Huang: The size of me actually give you a heart by region of the imaginary part of the of the action exist on an approximate the symbol.
Zichang Huang: And we are reading only arena and originally I say that if you really have the tango itself the.
Zichang Huang: Immigrant heart of the action will be the casting of that but, but that tempo actually forced to the critical point not not not forced to to the not forced to these we Sigma if you if you use the screen, one which is generated by this we Sigma actually the.
Zichang Huang: The metric part of the action it's not really a constant on the screen bring manifold.
Zichang Huang: And, but, but then The thing is, if you have a small small enough, we then the wherewithal to imagine.
Zichang Huang: The mental part of the actual be not large so that your calculations do works, this is one part of the control the other part of the country is this.
Zichang Huang: is how large this read things should be this is controlled by the flow kind so actually I generate this red one bye bye offload is this me Sigma with finance time team.
Zichang Huang: I mean if the tea is larger than this this red manifold will be large and the team is smaller than this recommended for will be small, which is.
Zichang Huang: Which is just, which is something just around the video point, and then the thing is actually if a half a large enough T, it will be enough because because I mean, because what you really do is what you really do is the integration that has this factor here is factor tells you that.
Zichang Huang: tells you that the point far away from the cradle point it's not important for the interval so then The thing is, if you have justified it is.
Zichang Huang: With the right choice, I mean in the algorithm you actually have you can actually try different tea and then fine if they if they can work to some numbers and then use the meanwhile the office converting to to do the result but, but the point is that you don't have to you, you can.
Zichang Huang: You can control the team to see which part to see to see if if the coins far away from your point.
Zichang Huang: contribute to to enable and actually because of this factor here that this point far away from the pain points not important than than the T, can you find out and somehow it can be not that so yeah so so actually this is two meters I used to to to to control this so called animation.
Zichang Huang: One one is the size of me and the other is the time of the flow.
Jonathan Engle: I see.
Jonathan Engle: So, so the fact that that the case very fast, this is just because the real part of the actions zero at the critical point but then it's just increasing when you go away from the.
Zichang Huang: Create it's because it's because of the equation, if you if you see that.
Zichang Huang: Okay, this is the.
Zichang Huang: opposite, it is.
Zichang Huang: The same as the action to compute the derivative of the action with respect to the floor financially, it is just a real and it is decreasing or flaxseed oil it doesn't have mindset is increasing.
Zichang Huang: yeah but The thing is, is as its flaws of weight and then the real part of the actual Israel.
Zichang Huang: will be launched, but the username is actually a small.
Zichang Huang: I see yeah somehow saying it is exponentially expressed.
Zichang Huang: For the contribution of the point far away from quitting.
Jonathan Engle: very nice yeah so that that statement doesn't depend on any large Dave.
Zichang Huang: rj yeah enlarge it actually it actually the situation it's actually more.
Zichang Huang: More clear because I mean really if you really put a London here.
Zichang Huang: Sure, but I had this Lambda actually indicates the speed up the flow how fast it is goes away, and if you have large London, the flow would be ideally to flow away, which gives you.
Zichang Huang: A very small to the minus X coordinate real action.
Jonathan Engle: But the point is you don't need the large Lambda for this approximation yes.
Zichang Huang: Actually, for my for my experience, I think the Lambda I mean for different Lambda the the flow time to be different.
Abhay Vasant Ashtekar: Right so from there you have you have like proper.
Zichang Huang: choice of tea then your poison.
Abhay Vasant Ashtekar: So, so do to depend on how far you are to go, I mean the vertical direction, but I can add if Lambda is small, you ever go much further, but call it a daily what you're not really saying is true, but, but in practice.
Zichang Huang: You have to I mean, in practice, I mean you might work Actually, I have to to find a way to choose the time of the floor, or the size of the red things are largely need to be to get enough to get enough approximation yeah but.
I think it.
Jorge Pullin: More questions oh.
Norbert Bodendorfer: The approximations you had this slide with the preservative and non-prescriptive effects we will discuss.
Norbert Bodendorfer: Yes, so I mean you have demonstrated very nicely that this method to compute the path in the world works very well for large spin so large Lambda.
Norbert Bodendorfer: Eventually, you will also be interested in computing the amplitude for small spins and i'm just interested whether there's a reasonable chance that this works, also for small spin spin under is one.
Zichang Huang: It for small spins 11744 is that actually the the terms that I dropped out may contribute to the integral so.
Zichang Huang: So I mean, at least for this algorithm.
Zichang Huang: I don't accept the head don't expect that will alumni he goes to one, it gives you exactly the right right right we talked.
Abhay Vasant Ashtekar: More than that right, you might expect the errors.
Abhay Vasant Ashtekar: More hundred or more percent right.
Abhay Vasant Ashtekar: dimensions.
You another.
Abhay Vasant Ashtekar: journey collecting could be as important as the terms Jackie.
Zichang Huang: And the thing is what I really think that will contributes to the.
Zichang Huang: I mean, will contribute to the integral for for the situation will alumni small, then the thing is.
Zichang Huang: In his hands, I mean for for this algorithm it just it just give you some.
Zichang Huang: Some corrections in the small spin situation it doesn't give you all the corrections and.
Abhay Vasant Ashtekar: So what i'm saying that what you're neglecting is the same as what you're keeping just because in going from minus infinity to zero neglecting, for example, that is probably.
Abhay Vasant Ashtekar: The same order as what you're keeping, so I would expect there to be hundred percent or more error, I mean.
Abhay Vasant Ashtekar: This is all going to be improved, but.
Norbert Bodendorfer: nobody's as you were saying before there's no free lunch and, as far as I gathered papers like this.
Norbert Bodendorfer: it's not expected that is left sets similar theory can solve the same problem completely I mean for general reasons.
Norbert Bodendorfer: And i'm just trying to understand whether kind of the region where it can solve the same problem for the amplitude here is just a very large spin regime and once you go to those spins all of these.
Norbert Bodendorfer: corrections that you neglecting your come up and, probably, you know finding all those critical points and studying all of them is probably as complicated as evaluating the military integral.
Abhay Vasant Ashtekar: I would agree with you, but but point is that you know.
Abhay Vasant Ashtekar: I think they're getting very good answers that even for 10 to the 600 the seven, and that is really pretty amazing, because that is like.
Abhay Vasant Ashtekar: You know the areas we're talking about are just 10 orders of magnitude about the Planck scale, which is, which is getting very, very good answers there, I think that would be damaging i'm agreeing with you.
Abhay Vasant Ashtekar: Completely know but but but i'm saying that what they're doing is still extremely interesting.
Norbert Bodendorfer: yeah sure I was asking where do we expect this fails, and.
Muxin Han: So so.
Muxin Han: The the are these four points of of.
Muxin Han: negligible.
Muxin Han: contributions, and if you go to smaller things and the point one there, there is existing algorithm to to get back to the point, one i'm just catching all the.
Muxin Han: Other critical point on the complex way and, and this is something we are working on and they only well, the only difficult parts are our two, three and four, and they are just released to.
Zichang Huang: The spin.
Muxin Han: And you have a release for the fact that in some form it's not into Rovers samples, so all these three point is somehow 52 to overcome.
Abhay Vasant Ashtekar: yeah but also you like to go very large distance in the time, as you know, we were talking before for the real part of action to supply the integral song, and so I think that's right.
Abhay Vasant Ashtekar: that's right to me, this is a this is this errors ips you know bus hundred percent or more, I mean they could be improved, but currently.
Muxin Han: Yes, yes, we are working on improving this.
Zichang Huang: And another thing is maybe maybe for the large thoughtful Smith lung small Lambda actually maybe use the recovering 15 days algorithm is better than this one, then that's I mean in the last item cadets as can only say see if we can combine the previous cope with this.
Zichang Huang: Is certain has a has a surprise to blessings.
Zichang Huang: and
Zichang Huang: If you say that for our region small under actually I I mean it has several several years there yeah.
Jorge Pullin: more questions.
Jorge Pullin: Okay let's thank the speaker again.