UK Nonlinear News,
and transport in many-particle systems
August 5-25 2002
By H.van Beijeren,
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
- 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
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Last Updated: 25th October 2002.