Exploring Quantum Chaos: Is it Truly Random or Deterministic?

[Crass_Oscillator]

Hi,

I was curious to know what the perception of quantum chaos is. It seems a bit on the fringe, but at the same time it seems interesting. An adviser I'm considering working for works on both solid state physics applications and does some theoretical work in quantum chaos, so I'm wondering if I should explore it or steer clear.

Thanks!

EDIT: I didn't know what to do for the thread prefix, I have advanced background so I don't really want watered down views on the subject but at the same time this is not a specific technical inquiry.

 

[jedishrfu]

For starters wikipedia has a survey article on it with references that you can read to further your understanding:

https://en.wikipedia.org/wiki/Quantum_chaos

It seems from the article that it is a valid research field with a lot of work already done and many interesting problems to investigate.

 

[secur]

An adviser I'm considering working for works on both solid state physics applications and does some theoretical work in quantum chaos, ...

This is not the question you're asking, and probably not the answer you want to hear. But forget quantum chaos, and go into solid state physics applications. A few years from now, rushing to an important conference, you'll grab a quick bite at McDonalds, where a quantum chaos theorist behind the counter will ask "do you want fries with that burger?"

 

[S.G. Janssens]

This is not the question you're asking, and probably not the answer you want to hear. But forget quantum chaos, and go into solid state physics applications. A few years from now, rushing to an important conference, you'll grab a quick bite at McDonalds, where a quantum chaos theorist behind the counter will ask "do you want fries with that burger?"

I think I understand what you are trying to say: Working in applied solid state physics will condemn one to the hasty consumption of greasy McDonald's food.

 

[atyy]

Quantum chaos is mainstream fringe, ie. it is a solid technical subject, but you may not need to know much about it for many physical applications.

For introductions, try


http://chaosbook.org/

https://arxiv.org/abs/0711.3939

 

[Crass_Oscillator]

Thanks. My suspicions, that the field is sort-of-valid but not in good shape appear to be correct. Theorists hired at EEE departments seem to be largely doing CS/AI (a bubble that I hope bursts soon) and theorists in physics seem to do topological materials.

Does anybody have an appraisal of the funding situation in computational materials physics (i.e. very applied), topological materials (i.e. applied from the point of view of a string theorist) and whether it's better to pursue a different field of EEE/applied physics/physics? I investigated computational biophysics for a bit and found it to be nauseatingly fluffy rubbish but that might be premature.

EDIT: There's also quantum information theory which seems both interesting and hot, and is at the interface of physics, electrical engineering, and computer science. However it frightens me that it's a whole lot of theory on computer architectures that effectively don't exist.

 

[secur]

@Crass_Oscillator,

Perhaps you should ask at the career guidance forum https://www.physicsforums.com/forums/career-guidance.193/. They're more likely to know about non-technical issues like funding situation. FWIW QIT is promising, quantum computers may be viable in a decade or two, IMHO.

 

[A. Neumaier]

Quantum chaos is the study of quantum effects associated to systems that classically behave chaotically. Research on it is publishable - but it is soft theoretical physics in the sense that there are no hard facts but lots of computer studies, with in my view relatively meager results. Classically, the onset of chaos and the related breakdown of KAM tori are theoretically and computationally well-understood results, with lots of strong and nontrivial theory.

On the quantum side, neither of these exist; not even a clear definition of what quantum chaos is supposed to be - in spite of 40 years of research done on it!

Roughly speaking, quantum chaos means that at sufficiently high energies it becomes imposssible to assign (in terms of quantum numbers) all levels observed spectroscopically or computed by quantum chemistry. Energy levels with a full set of quantum numbers corresponds semiclassically to a special KAM torus (the analogue of a Bohr-Sommerfeld quantized orbit to more than one degree of freedom), which exists at energies below the first saddle point reachable from the starting point of a trajectory. The corresponding squared amplitudes of wave functions display (in 2 DOF cases) a collection of modes forming a more or less deformed grid pattern. When the classical system is sufficiently chaotic, the pattern develops what has been termed scars. But there is hardly any theory supporting or explaining all this.

Theory begins only at the point where no regularity in the energy levels (and the wave functions) is left and one can treat the Hamiltonian as a random matrix. Then random matrix theory applies phenomenologically; no proofs seem to exist. Random matrices have a good theory and many interesting results. However, the connection to quantum chaos is again very loose, with no theory to lend support.

It is fine to learn a little bit about the subject, but I wouldn't recommend it as a subject for a PhD or later research.

 

[A. Neumaier]

quantum computers may be viable in a decade or two

I doubt that a lot. At present they can hardly do more that multiplying 3*5. See also the discussion at https://www.physicsforums.com/threads/status-of-quantum-computing.880521

The only realistic application of quantum information theory in the near future is (possibly) in cryptography.

 

[secur]

... quantum computers may be viable in a decade or two ...

I doubt that a lot.

Even if there's only a .0000000001 chance, still they may be viable :-) Anyway if enough people who decide funding are optimistic about it, that's good enough career-wise.

 

[Crass_Oscillator]

Thanks for your detailed response A.Neumaier. You refer to what I assume are formal mathematical proofs repeatedly. Wasn't quantum mechanics itself relatively informal pre-Neumann, and even after that? To frame it differently, do you think it is simply the case that quantum chaos does not clearly connect to empirical reality, or that its connections are too informal, or do I not understand what you are saying? Personally if the phenomenology makes unambiguous empirical predictions that's interesting to me.

When I completed my physics bachelors I thought quantum computing was a hype bubble and still suspect so, but unfortunately there do not seem to be any fields of theoretical physics which have a healthy theory/experiment relationship left. However this is a question for a different thread.

 

[A. Neumaier]

Thanks for your detailed response A.Neumaier. You refer to what I assume are formal mathematical proofs repeatedly. Wasn't quantum mechanics itself relatively informal pre-Neumann, and even after that? To frame it differently, do you think it is simply the case that quantum chaos does not clearly connect to empirical reality, or that its connections are too informal, or do I not understand what you are saying? Personally if the phenomenology makes unambiguous empirical predictions that's interesting to me.

When I completed my physics bachelors I thought quantum computing was a hype bubble and still suspect so, but unfortunately there do not seem to be any fields of theoretical physics which have a healthy theory/experiment relationship left. However this is a question for a different thread.

I was not referring to mathematical proofs. Yes, KAM is a mathematically rigorous result, but that's here besides the point. On the quantum side there is not even an informal nonrigorous theory - nothing predictive, just computations and informal generalization of what these seem to suggest. It is much worse than what existed in 1931 about informal (but quite healthy) quantum mechanics. All there is are relations valid in the classical limit, assuming all quantum numbers (corresponding to a full set of classical action variables) are good. Apart from that, just looking at computations and bla-bla about its interpretation. Nothing predictive at all.

Go into quantum chromodynamics and its descendants (chiral perturbation theory etc.). Scattering theory is there well understood, but reproducing the observed spectrum of particles from the foundations is still a very big challenge!

 

[vanhees71]

I doubt that a lot. At present they can hardly do more that multiplying 3*5. See also the discussion at https://www.physicsforums.com/threads/status-of-quantum-computing.880521

The only realistic application of quantum information theory in the near future is (possibly) in cryptography.

Hm, I'd not be so pessimistic. It's amazing what is done in condensed-matter physics these days, and quantum cryptography is already reality!

 

[A. Neumaier]

Hm, I'd not be so pessimistic. It's amazing what is done in condensed-matter physics these days, and quantum cryptography is already reality!

Even amazing condensed matter physics is still far from quantum computing. And quantum cryptography exists but is not used on a significant scale.

 

[vanhees71]

That is indeed true to, but as I said, I'm not so pessimistic concerning the development of new technology. Who knows, what happens in 20-30 years in this quickly developing field?

 

[Crass_Oscillator]

Perhaps we need a new thread, but my fear is that quantum computing will go the way of fusion physics. Tremendous over hype (in this case including one of the most over hyped companies in human history, Google!) causes major setbacks in the near future.

Obviously with ITER plasma physics is still trucking along, but it's not as exciting as it used to be.

 

[radium]

Quantum chaos is an incredibly hot topic in more field theoretic condensed matter and holography (black holes and large N matrix theories saturate a "chaos bound" proposed by Maldacena and collaborators).

 

[Crass_Oscillator]

Quantum chaos is an incredibly hot topic in more field theoretic condensed matter and holography (black holes and large N matrix theories saturate a "chaos bound" proposed by Maldacena and collaborators).

That's really interesting, thanks for sharing. Is this dependent on AdS/CFT?

 

[radium]

No, you can calculate stuff like the Lyapunov exponent in large N QFTs (matrix or vector). However, it has motivated proposals of holographic duals for certain strongly coupled matrix large N theories which saturate the chaos bound.

 

[dakoder]

Hi,

I was curious to know what the perception of quantum chaos is. It seems a bit on the fringe, but at the same time it seems interesting. An adviser I'm considering working for works on both solid state physics applications and does some theoretical work in quantum chaos, so I'm wondering if I should explore it or steer clear.

Thanks!

EDIT: I didn't know what to do for the thread prefix, I have advanced background so I don't really want watered down views on the subject but at the same time this is not a specific technical inquiry.

I would like to hear your views on 'langtons ant wave equation'
Langtons ant has been proven to be chaotic, Turin complete and now there is a also a wave equation for it.

 

[DrClaude]

I would like to hear your views on 'langtons ant wave equation'

Do you have a reference.

 

[Crass_Oscillator]

Do you have a reference.

Seconded, although since posting this thread I opted to work in quantum transport in materials rather than quantum chaos, a more mundane and straightforward discipline, so I don't know if I'll have much to say about Langton's ant.

 

[atyy]

http://www.scholarpedia.org/article/Bohigas-Giannoni-Schmit_conjecture
Bohigas-Giannoni-Schmit conjecture
Denis Ullmo (2016), Scholarpedia, 11(9):31721

https://arxiv.org/abs/1101.3116
Physics of the Riemann Hypothesis
Daniel Schumayer, David A. W. Hutchinson

https://arxiv.org/abs/1503.07538
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
C. Gogolin, J. Eisert

 

[Leo1233783]

Today, one can play with hardawre random generator on computers. Random signals ( noise ) coming from the hardware are captured by ( some versions of ) /dev/random to produce a high level of entropy and to output random datas. But with some tricks, the driver can output ( slowly ) the noise measures without classical amplification based on other inputs. There is also the Gisin method using the camera device. Is it quantum data? Since we cannot hope to build a kind of entanglement, how physics may help to discriminate quantum from deterministic data ? I tried quantum tunnelling simulation efficiency without finding any differences.