Time: February - March, 1999

Scope of the workshop:

The workshop is concerned with the dynamics of systems involving many interacting particles. One central theme is the emergence of long-lived structures on a macroscopic scale, i.e. on a length scale large compared to the interparticle separation,  and on a time scale long compared to their interaction time. Physically the microscopic dynamics is  governed by the Schrödinger equation or by Newton's equations of motion. However, it has been realized over the past decades that it is often more useful to model on a somewhat coarser scale. The workshop will focus on this problem.

 As an illustration we list a few examples. In recent molecular dynamics simulations of transport coefficients an external perturbation is applied to the system which is driven to a  nonequilibrium state. This state is made stationary by the addition of a  non-Newtonian thermostatting force to the classical microscopic equations of motion.  In spite of the time-reversible nature of this thermostat such systems are macroscopically irreversible as is explained by the appearance of fractal structures in phase space. Theoretical concepts, originally developed for Anosov flows, become applicable. Coarse graining provides a link to stochastic dynamics  and allows the computation of the macroscopic rate of irreversible entropy production. Statistical physics provides also a wealth of other models with stochastic dynamics.  In detailed-balance models one controls mathematically the  emergence of nonlinear diffusion equations and of the incompressible  Navier-Stokes equation depending on how many conservation laws are imposed microscopically. Of much recent interest are driven stochastic systems, like the roughening of growing interfaces,  surface diffusion, aggregation, granular flow, and low-noise-driven  threshold dynamics.  In deterministic lattice gas automatons realistic  microscopic interactions are waived: particles move on a spatial grid and have simple collision rules involving only a few particles. Lattice gases proved also very useful for flows in complicated geometries or at high  Reynolds numbers. Another important area is spatio-temporal chaos. Here the underlying " microscopic" dynamics is given by partial differential  equations such a s the Kuramoto-Shivasinsky equation, or, in a discretized  version, as coupled map lattices.

Despite their different appearance, these fields share theoretical  methods and ideas. The workshop is aimed at a fruitful interaction between these topics.  The aim is an equally balanced discussion of methods and concepts from theoretical and mathematical physics.

A topical conference is planned for the last week in February.

Topics:

• Hamiltonian dynamics
• Thermostatted stationary nonequilibrium systems
• Spatially extended dynamical systems
• Stochastic dynamics