UK Nonlinear News, November 2002

Microscopic chaos and transport in many-particle systems

Dresden, Germany August 5-25 2002

By H.van Beijeren, R.Klages, P.Gaspard and J.R.Dorfman

This conference was focused on the connections between dynamical systems theory and statistical physics with a major emphasis on the description of nonequilibrium systems. A fundamental problem in this field is to analyse the fractal properties of nonequilibrium steady states as generated by microscopic chaos in the motion of atoms and molecules composing fluids. In particular, one tries to find relationships between characteristic quantities of chaos and transport properties and to assess their validity.

Some of the most central topics were

The Evans-Cohen-Gallavotti fluctuation theorem.
The "founding father" D. Evans gave a very good review of the various versions of this important theorem; G. Gallavotti discussed some very interesting applications in hydrodynamics far from the microscopic realm for which the theorem was envisioned originally, and C. Maes derived a quite general version of the fluctuation theorem valid for Hamiltonian systems coupled stochastically to heat baths. Z.Kovács showed that the fluctuation theorem still holds in certain specific cases where not all mathematical conditions are satisfied.
Hydrodynamic modes, generalisations of hydrodynamic modes and other long wave length collective modes.
P. Gaspard showed how hydrodynamic modes may be constructed for various systems ranging from simple toy models to many interacting particles. J.R. Dorfman and I. Claus lectured on the same topic and D. Wojcik and T. Prosen shed some light on how to generalise these concepts to quantum mechanical systems. The subject of how to generalise hydrodynamics and hydrodynamic modes to low-dimensional systems in which transport is anomalous was treated by P. Grassberger, T. Geisel, D. Isbister, Y. Klafter, G. Radons and S. Tasaki. H. Posch reported on collective very slowly growing modes in the Lyapunov spectrum of many particle systems. Theoretical treatments of this were reported by M. Mareschal, A. de Wijn and T. Taniguchi, but so far none of them is capable of completely explaining the eigenvalue spectrum observed in the simulations.
The physical status of mathematical thermostats such as the Nosé-Hoover and the Gaussian ones remained much disputed. R. Klages gave a good review of this subject and it also came up in the talks by Da .Evans, D. Panja, G. Morriss, S. Hess, and W.G. Hoover as well as in many private discussions.

Introductory lectures were provided by O. de Almeida, P. Cvitanovic, C. Maes, D. Evans and P. Gaspard. Younger people could present their posters in form of 4-minute talks during a special workshop session, and they competed for book awards for the three best posters. Newcomers with very interesting contributions were N. Davidson, who does experiments on atom-laser interactions, B. Li and D. Alonso, both working on non-dispersing but nonetheless diffusive billiards, and H. Larralde, who reported on billiards with rotating scatterers. The 86 conference participants were from 22 countries, 18 of them were Ph.D. students, 22 postdocs, and 11 were active participants from the MPIPKS.

This conference was very valuable as a platform for the exchange of ideas. It sharpened the contours of problems to be solved yet, of issues on which the opinions are still divided and of directions to follow in the future. The excellent setting and organisation contributed much to its success, and the full program could be carried through despite the serious flooding that occurred in Dresden. The main scientific results of this conference will be published as proceedings in a special issue of Physica D.

More information about this conference (final program, photos, etc.) can be found on the conference webpage.

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Last Updated: 25th October 2002.