Uniquely clear description of What entropy IS.

Wouldn't A interaction be defined as U A U dagger the other way around since we initially started with U dagger????

Related to the "information scrambling" video, is Anderson localization one way to prevent the scrambling of quantum information? Can we fully reconstruct the history of the state at the center of the lattice?

In the Aubrey-Andre model, can we predict where the localized sites would be?

Can information scrambling be de-scrambled? or is it fundamentally irreversible (thermo 2nd law connection)?

Can "scrambling propagation speed" covering larger and larger subsystem be defined as a meaningful quantity?

Is the scrambling of information inevitable in a many-body quantum system? How does system size play into this?

Hello, thank you for this video. I had a question. I am currently a CS student, and I am exploring all fields related to my expertise, and currently I am so curious about this path, computional science; But I don't find any good video. I want to know about one's experience who really worked something. Can you please fill a video and explain what is and how is your job, nad how can we enter this field?

This reminds me of a science fiction book I just read called quantum xy, about a group of Silicon Valley engineers who sought to create an ai learning model with moralistic principles. The system learned from the input commands of known moralists and grew its network based on the networks of these individuals. I can’t remember the author but I believe it was released in 93’ early 93. Way ahead of its time.

MatLab kinda slow

Amazing

I just got my bachelor in Fundamental Physics, and i chose to continue a Master degree in Computational physics, we'll start in September

hello, thanks for the vid! For reference, Fortran dependency management is getting better. See, for example, the fpm package manager, in development by the fortran-lang group. Just in case anyone wants to learn more. Fortran ftw!

Oh yes, didnt probability came way later after algerbra and like a bunch of really advanced maths.

Very well described. But anyways, it is frankly astounding that we can make accurate predictions about so many complex systems by using simple arguments in statistical mechanics!

Very nice video! I am currently a physics graduate student who is trying to get some knowledge of the computational methods. This subject is really intimidating at the early stage of learning. I really liked to hear different people describing them in they own way., which always give a me another perspective to see them. Hope I could get into my Phd in the future and help others like you did! Two questions, 1. at 18:12, is there should also be a exponential Lamda for |Emax> outside the bracket? 2. How could subtract a large enough C from the Hamiltonian helps to guarantee what we find is the ground state? Could you elaborate a little more?

thx for the nice explanation and greetings to your cat

@4:00 note that a lot of the pre-theoretical difficulty in quantum → classical comes from this (I think false or misleading) language framing. The Schrödinger equation does *_not_* describe the time evolution of the real physical system. It describes the effective time evolution of the Hilbert space "state" that is our model for the system. You can impose a realist view then, just do not take the ket as "the real".

As a scientist programmer, I really disagree about the comments over C. Although it is not usually the way-to-go, nothing is better than C. Nothing is faster than C. Nothing is more computationally efficient than C. So being able to delegate certain parts of your tasks to C code written by you is sometimes the most reasonable choice.

Thank you very much for all this. Burning out is the major challenge for PhD students. Really great advice! Going through the fastest path is usually the most reasonable choice, for sure. Nothing to add, great video!

15:01 This assumption is weird for me because it almost assume thos A_{m,m} are constant, so no matter what kind of measure( c_{m,m} or uniform) you use to compute expected value, the result is the same. So it's almost trivial because we can use what ever disdtribution we want, not necessary those given by stat mech. Or maybe there's more detailed argument about this assumption?

guru thanks for teaching ❤️

thanks for the very interesting video. Why is temperature defined via 1/T=dS/dE, would it be easier to say T=dE/dS? Is it because entropy changes as energy changes but not necessarily the other way around? Another words entropy is the dependent variable.

Don’t mix 3-body problems with probability 😊

amazing video, gave me clarity on the topic. Thanks for the help!

Python is similar to a markup language. If you have a problem, you say to python call the library written in another language. That means you have to learn python and a some libraries. One for calculation, one for visualization at least. You talked about the wired point syntax. Actually it is a strength of Julia.

Just come across negative temperatures seen several explanations after watching this things just went click, nice one!

The difficulty with Julia isn't the language, but working out a good developer workflow with the immaturity of the packages. There's also the case that if you're learning data science, chances are that the courses use MATLAB or Python, so you pretty much have to learn those languages anyway. I think this explains somewhat why Julia has failed to gain in popularity.

Julia can call pyplot... Moreover, you get the ITensors library. Many Body Physics and Julia hands down!

Julia is absolutely great, if you don't need (or want) to rely on packages written by others. Its dynamically typed code, when used in functions, is super fast (one does not need to declare types, just like in Python or MATLAB), while its type system is used to extend functions or create "smart" data types. There is an extensive plotting suite, called Makie, that allows you to make multi-panel plots and interactive dashboards. You can also use notebook workflow. One slight disadvantage of Julia is its "time to first plot", waiting after starting up Julia and running the code for the first time, which used to be a big issue but has been improved a lot since v1.9. However, if you keep the REPL open, subsequent execution works instantly. I chose to learn Julia after coming from C, IDL/PV-WAVE and Scilab. Julia got the necessary packages I needed to get going with my data. I considered that I rather wanted to gain expertise in the best language for my job, than feel a beginner in Python working around slow and possibly unappetizing code already written by colleagues. Although most of my colleagues still remain on the fence as MATLAB and Python users, one of them let me know he tried out Julia and was pleased to find Julia can actually still interact very smoothly with Python (via PyCall).

Question, how much does this conservation of information theoretically applies to properties that are more familiar to a human scale. For example, let’s say you have two glasses of pure water and you mix them. Could you theoretically derive, through quantum mechanics, all the particular atoms which made of each glass?

The issue is vast majority of developers do NOT do novel things. I worked for amazon for many years, trust me

@14:20 OOP was introduced in Fortran 90 (released in 1990). It's... not great, but it's there.

Thanks a ton Jonathan could please provide the resources or textbooks or lecture notes where I can dive deeply into the concepts of these transformation and Quantum Many Body Hamiltonian.

Python is kidding, it just for who dont no c, rust, nime and ....

4:55 - If the kets transform under U_{H_0, t)}^{/dagger}, then in the expectation value, the bra should transform under U_{H_0, t}, right?

Please make a introductory series for beginners in computational physics

12:33 about in static languages such as C++ supported by GCC "[needing to worry about] garbage collection" (GC), I believe it's meant that you have to throw it out (and allocate manually), i.e. you only have manual memory management, unlike in GC-based languages like Julia (and Python). Yes, true for C, Fortran, less so for C++ and Rust (RAII gives similar benefit), but you CAN add GC to C and C+ (commonly done, e.g. most web browsers do that). GC-based like Julia (or in effect when you add GC in C++) IS easier. It can have downsides that are all avoidable in Julia, i.e. it allows avoiding heap-allocations (or preallocating there) to to help with real-time or just to eliminate small (unpredictable) overhead. [About Fortran not having OOP later at 14:20, is historically true, but it actually has OOP by now in recent versions, but still probably not much used, or too idiomatic, at least in vast majority of old/current code. And not like OOP is better... there or in C++ or Python, it's not for speed, Julia does away with traditional OOP, but such can be added with packages.]

Nice presentation. I first came across the Legendre transform in Thermodynamics without an explicit reference to what it entailed. "A graphical derivation of the Legendre Transform" by Sam Kennerly (12 April 2011) and "Making sense of the Legendre transform" by Zia, Redish & McKay, American Journal of Physics, vol. 77, (7), July 2009 present enlightening discussions on the Legendre Transform.

at 0:43 you said we assign probabilities to the microstates, this doesn't make sense because we assume in stat mech that each microstate is equally probable, and the most probable *macrostate* is that which has the most microstates

very much interesting lectures. Please mention the name of book from where the lecture have been taken

Certainly true today, but Something tells me this video might not age well haha

M ETH

C/C++ are certainly starting to show their age. C++ in particular looks like someone who has had too many plastic surgeries to still look young.

I would like to learn some coding for MPS as well as MPO which also work for subspaces (like in half-filling sector) in MATLAB. Any suggestions?

As a computational materials scientist wanna just to thank you for this video. I hope I had seen it as I started my journey.

Not NottingHAM (as in ham sandwich) but "NottingUM" (as pronounced in U.K.)😊

Thanks for the tips! Is there any language/software that matches Mathematica's optimization for symbolic calculation? From what I understand, theoretical physicists depend heavily on this.

Amazing job man, keep it up!!!!

Mind the gap. Applicability of statistical and stochastic processes analysis is limited by characteristics of the underlying dynamical system. We have our brains (all brains at large, not only human) to predict the future. Dominating hypothesis is, we do it by means of Bayesian statistical inference. Trying to model the underlying dynamical system gives us an edge over pure statistical and stochastic modelling. It can predict such surprising effects like reversal of "causality"; swap of antecedent and lagging variable (in, say, predator-pray cycles). In other words, considering the dynamical system underlying the process might give you an edge even over these ML/AI systems, that I know about.