Current scope of Chaos theory and non-linear dynamics?

Question

I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like weather etc? I asked this question, because I browsed through the websites of the physics departments of a few renowned universities (MIT, Princeton, Caltech) etc, but nowhere it mentioned research in these areas.

This post imported from StackExchange Physics at 2014-12-31 12:07 (UTC), posted by SE-user user7757

Comments

Quick suggestion: Look at papers in Nonlinearity, iopscience.iop.org/0951-7715, and in JMathPhys to see where the authors of papers that are interesting to you come from. You should have access at least to JMathPhys through your university library. Look for what other journals those authors write in, and go through the roots and branches progressively. Hopefully you have or can find enough time not to have to hurry. This stuff is often studied as a separate discipline more in Math departments than in Physics departments, even though many Physicists know it intimately.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user Peter Morgan

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@PeterMorgan: can i extend the question to include quantum chaos and disordered systems? Could you provide me with some names in this field, and some universities which has research groups working on quantum disordered systems?

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user user7757

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have a look at this list from MIT web.mit.edu/redingtn/www/netadv/Xcomplexit.html . Note that chaos is often coupled with complexity

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user anna v

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This seems like a too broad list question.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user Qmechanic

Answer 1

Yes, there is investigation.

Some random names on the field (more on the physics side, NO specific order): Carl Dettmann, Tamás Tél, Ott, Ying-Cheng Lai, Adilson Motter, Celso Grebogi, Holger Kantz, Alessandro Moura, Eduardo G. Altmann, etc, etc, etc.

A quick search on some of these names should help you to find some recent papers on what is being done (not restricted to!).

Some specific topics on the subject with some activity:

Billiards, Transient chaos, Hamiltonian systems, quantum chaos, control theory.

Do not be biased by this information, use it has a shortcut to search more and more. It is not meant to represent anything in terms of importance, quantity or quality of the research.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user J. C. Leitão

Comments

can i extend the question to include quantum chaos and disordered systems? Could you provide me with some names in this field, and some universities which has research groups working on quantum disordered systems?

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user user7757

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@ramanujan_dirac The concepts of chaos theory and nonlinear dynamics are also useful to study the renormalization group flow beyond a single scale invariant fixed point as I hinted to in this answer.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user Dilaton

Answer 2

There is of course research going on. For example the field of billiards is still very active. People study e.g. billiards with non-trivial reflection rules.

In general this is done in Math departments rather than Physics, although there are a lot of physicists working there.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user user9886

Comments

can i extend the question to include quantum chaos and disordered systems? Could you provide me with some names in this field, and some universities which has research groups working on quantum disordered systems?

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user user7757

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Some names straight from mind and w/o completenes and order: A. Buchleitner, F. Haake, K. Nakamura, H. J. Stöckmann, M. Gutzwiller and many more.

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user user9886

Answer 3

Myself is working on this area and I will tell you why I found it fascinating. This area contain many interesting new mathematics, for example if you analyze dissipative chaotic system you will encounter fractals in phase-space. Fractals are the beautiful mathematical objects which cannot be treated with standard differential geometry.This type of mathematics is simple to understand in the numerical sense, hence you may think that the subject is simple. Once you try to track the nonlinear problems analytically this is more challenging. Often people relay on numerical computation. If you want do the research in classical chaos you should know about the chaotic maps and related things. Mainly mathematicians are working on this area and they call it "Dynamical system theory". Prof. James Yorke is one of the reputed person in this area. If you think about Quantum Mechanics there is an area called Quantum Chaos. The Gutzwiller trace formula (Periodic orbit theory) and Predrag Civitanovic's Cycle expansion are the hottest topics.Cycle expansion can be utilized to study the fluid turbulence. Related to the periodic orbit theory people are trying to find the zeros of zeta functions using a quantum hamiltonian. If you can quantize H=xp properly then you can become a reputed guy in this area. In short, quantum chaos have applications in number theory. Jon Keating and Michel V. Berry are the reputed figures in this area. Then it comes the chaotic billiard, Sinai Billiard and the Bunimovich stadium are the few examples of it. Yakov Sinai, Leonid Bunimovich, and Marko Robnik are the reputed figures in this area. This topic has intimate connection to the statistical mechanics and the ergodic theory. Chaos theory also appear in the context of Renormalization group theory. Related to quantum billiard you can study the Quantum unique ergodicity, Quantum Scars etc. Terence Tao, Eric Heller etc. are working on this topic. Terence Tao works in the area of Random Matrix theory which is an area of pure Mathematics related to Quantum Chaos. By the way, Madan Lal Mehta and Dyson had done a great contribution to Random Matrix theory. Actually Eugene Wigner had started the idea of using Radom Matrix theory in Quantum Mechanics.

Now people are also studying chaos in connection with Quantum Entanglement (Entanglement and Chaos). In relation to quantum gravity, Gerard 't Hooft is studying the deterministic quantum mechanics using the ideas of cellular automata. (Cellular automata and iterating function system(IFS) appear in connection with fractals). There are other people like Laurent Nottale who study the non-differentiable space-time and the emergence of quantum mechanics from it. Some people use the geodesic deviation equation from general relativity to quantify the chaotic property. In short this is a vast and rich topic and you can work in in all areas of physics to apply the ideas of Chaos theory and the nonlinear dynamics.

There are many other topics and interesting people in this field and this information is my limited point of view about this topic!

You can look at University of Maryland, Georgia Tech, University of Bristol UK etc where they have good groups. If a university has a reputation, it doesn't mean that in all areas they are strong enough !!!

This post imported from StackExchange Physics at 2014-12-31 12:08 (UTC), posted by SE-user Sijo Joseph