A Quantum Chaos: Expert Discussion and Q&A

[MathematicalPhysicist]

TL;DR Summary

Are there any experts in Quantum Chaos in these forums?

I might have a few questions about this topic in the future.
So I am just asking if there are any experts on this topic here?

Thanks in advance!
BTW I asked also in physics stackexchange why they don't have a tag of QC, but you know how that site is...

 

[Cthugha]

I have published a few articles on QC, but I am not sure whether this renders me an expert. I am an experimentalist and therefore my knowledge is rather specialized. One of the articles was the following:

QC and antiunitary symmetry breaking in Rydberg excitons

A more accessible news and views article about the results can be found here:
Probing Quantum Chaos

It has been a while since I dealt with that stuff, but let me know whether I can help.

 

[MathematicalPhysicist]

I have published a few articles on QC, but I am not sure whether this renders me an expert. I am an experimentalist and therefore my knowledge is rather specialized. One of the articles was the following:

QC and antiunitary symmetry breaking in Rydberg excitons

A more accessible news and views article about the results can be found here:
Probing Quantum Chaos

It has been a while since I dealt with that stuff, but let me know whether I can help.

Ok thanks.
Though my questions are more with a mathematical flavour.
I'll probably cover the textbook: https://math.berkeley.edu/~evans/semiclassical.pdf
And other references that I have or will find.
So mentors, I plan to post to this post so until when can I post to this thread? I mean before it's closed.

 

[Cthugha]

Well, quantum chaos is a broad (and somewhat ill-defined) topic which is maybe best described as the quantum mechanics of classically chaotic systems. Accordingly - even from the math point of view - there are several approaches and it is not easy to suggest some references unless one gets a rough impression of what you are interested in.

I guess, the standard books would be Gutzwiller's "Chaos in classical and quantum mechanics" and Haake's "Quantum signatures of chaos". However, there are of course more modern developments depending on whether you are interested in random matrix theory, measures of level spacing statistics, periodic orbits, number theory and the Riemann zeta function or whatever. This is a huge field. Are you interested in some certain aspect?

 

[Haborix]

Just to follow up and reiterate Cthugha's comment that the subject is broad and somewhat ill-defined, my impression trying to learn about quantum chaos some years ago was that you were going to have to be satisfied with learning a collection of "neat tricks." To the extent there is anything deep to be said about quantum chaos, it always seemed to be bound up in serious and, often, unresolved cutting-edge mathematics. There is no Theory of Quantum Chaos so to speak.

I remember a book on random matrices by Mehta that I thought was good.

 

[jim mcnamara]

@MathematicalPhysicist

Threads do not automatically close after some specified time. We do proactively close threads that have problems.

 

[MathematicalPhysicist]

Just to follow up and reiterate Cthugha's comment that the subject is broad and somewhat ill-defined, my impression trying to learn about quantum chaos some years ago was that you were going to have to be satisfied with learning a collection of "neat tricks." To the extent there is anything deep to be said about quantum chaos, it always seemed to be bound up in serious and, often, unresolved cutting-edge mathematics. There is no Theory of Quantum Chaos so to speak.

I remember a book on random matrices by Mehta that I thought was good.

I have the book of Mehta on Random Matrices (hard cover).
In the course that I had taken on Intro to Random Matrices which covered Anderson's and Zeitouni's intro book (which I also have hard cover somewhere in my room) was from the maths department.
I failed the course since I thought I could learn it by myself from the book, and I didn't want to attend class since it was hot there I mean the air condition doesn't work in the winter which is really hot here (I mean in the university).
I didn't finish reading the book by Zeitouni, one day I may return to it and after that to Mehta's. (the lecturer seemed terrified by the physicist's book, or so it seemed to me...).

Ah being a MathematicalPhysicist... the best of both worlds.

 

[MathematicalPhysicist]

Just to follow up and reiterate Cthugha's comment that the subject is broad and somewhat ill-defined, my impression trying to learn about quantum chaos some years ago was that you were going to have to be satisfied with learning a collection of "neat tricks." To the extent there is anything deep to be said about quantum chaos, it always seemed to be bound up in serious and, often, unresolved cutting-edge mathematics. There is no Theory of Quantum Chaos so to speak.

I remember a book on random matrices by Mehta that I thought was good.

Perhaps after I am done reading I could build the theory of QC so to speak.
Until then, just learning.

 

[MathematicalPhysicist]

Anyway, it's great that I have at least two posters who may be able to help me.
BTW, I have Gurztwiller's and Signatures of chaos.
Though from reading the preface of Gurztwiller a few years ago I understood that there are no rigorous proof in this book, i.e not detailed proofs, I haven't read past the few pages on classical analytic mechanics which I know already from Lagrangian and Hamiltonian mechanics from my B.Sc studies.
But it's always good to refresh.

 

[atyy]

http://chaosbook.org/
Chaos: Classical and Quantum
Predrag Cvitanovic, Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay
Part 5 of the book is about quantum chaos

It seems that there are some rigorous theorems related to the Berry-Tabor conjecture
https://people.maths.bris.ac.uk/~majm/bib/3ecm.pdf
The Berry-Tabor conjecture
Jens Marklof

For example, Marklof mentions
https://annals.math.princeton.edu/wp-content/uploads/annals-v161-n2-p03.pdf
of which I cannot understand a single word, so it must be rigorous

 

[MathematicalPhysicist]

http://chaosbook.org/
Chaos: Classical and Quantum
Predrag Cvitanovic, Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay
Part 5 of the book is about quantum chaos

It seems that there are some rigorous theorems related to the Berry-Tabor conjecture
https://people.maths.bris.ac.uk/~majm/bib/3ecm.pdf
The Berry-Tabor conjecture
Jens Marklof

For example, Marklof mentions
https://annals.math.princeton.edu/wp-content/uploads/annals-v161-n2-p03.pdf
of which I cannot understand a single word, so it must be rigorous

Yeah I know all of these; but if I have any further questions, I'll know to ask the two posters.

 

[atyy]

Also, Wikipedia has an interesting article on quantum scars, not sure whether any results here are rigorous.
https://en.wikipedia.org/wiki/Quantum_scar

 

[MathematicalPhysicist]

Also, Wikipedia has an interesting article on quantum scars, not sure whether any results here are rigorous.
https://en.wikipedia.org/wiki/Quantum_scar

Yes, it seems all this is really quite nonrigorous.

I hope someday to make some sort of unification between quantum chaos, quantum cosmology, quantum gravity and quantum field theory.

I know it sounds childish, but who knows?

Quantum is the headline...

 

[atyy]

Like this?

https://member.ipmu.jp/yuji.tachikawa/stringsmirrors/2019/1_b_swingle.pdf
Quantum Chaos and Scrambling: Recent Developments (video)
Brian Swingle
STRINGS 2019

 

[MathematicalPhysicist]

Hi @atyy I don't want to be harsh, but I understand that you are a biologist.

[Sexist comments deleted by the Mentors]

 

[atyy]

@MathematicalPhysicist I have reported your sexist post.

 

[MathematicalPhysicist]

they looked nice, and that was a compliment.

 

[Demystifier]

Hi @atyy I don't want to be harsh, but I understand that you are a biologist.

[Sexist comments deleted by the Mentors]

As far as has been revealed in this forum so far, @atyy is a male, has a degree in both biology and physics, and has a very deep knowledge of math.

 

[martinbn]

Hi @atyy I don't want to be harsh, but I understand that you are a biologist.

[Sexist comments deleted by the Mentors]

Since we are off topic, just wanted to point out that the reason the number of females is low is not what your post implies. There was one article, which I cannot find, about the difference in numbers of girls and boys interested in maths in high school. It had an example of one country that since the 50's has had about eqaul number of girls and boys interested in maths, doing competitions, winning competitions, going to uni to major in maths. My experience says that their data was accurate.

 

[MathematicalPhysicist]

As far as has been revealed in this forum so far, @atyy is a male, has a degree in both biology and physics, and has a very deep knowledge of math.

Ah, sorry I didn't know he double major with physics.
I thought I remembered that he said he is a Biologist.

 

[MathematicalPhysicist]

Since we are off topic, just wanted to point out that the reason the number of females is low is not what your post implies. There was one article, which I cannot find, about the difference in numbers of girls and boys interested in maths in high school. It had an example of one country that since the 50's has had about eqaul number of girls and boys interested in maths, doing competitions, winning competitions, going to uni to major in maths. My experience says that their data was accurate.

From my experience the most advanced courses in maths and physics lack female students.
They do appear in the basic courses and intermediate.

 

[martinbn]

From my experience the most advanced courses in maths and physics lack female students.
They do appear in the basic courses and intermediate.

My point was, that there are places where that is not so, therefore the reason is not difference of abilities.

 

[Motore]

From my experience the most advanced courses in maths and physics lack female students.
They do appear in the basic courses and intermediate.

In our country there is an equal amount of female students, undergrad, grad, doc, post doc in math and physics.
We have a lack of them in mechanical and electrical engineering.

 

[MathematicalPhysicist]

In our country there is an equal amount of female students, undergrad, grad, doc, post doc in math and physics.
We have a lack of them in mechanical and electrical engineering.

In my country it's exactly the opposite.

 

[Demystifier]

In my country it's exactly the opposite.

May I ask what country is that?

 

[fresh_42]

This topic might lead to chaos, but not to quantum chaos.

Thread closed.

 

[berkeman]

Since this thread has veered off-topic, it will remain closed (and an inappropriate comment has been redacted).