Dynamics in Physical Models

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

The project is devoted to dynamical systems of physical origin, including Lorentz gases (both in equilibrium and under external forces), hard ball systems, billiards, ideal gases with a massive test particle, and open Hamiltonian systems. Most of these are known (or expected) to have chaotic behavior. Due to recent works of D. Dolgopyat, D. Ruelle, Ya. Sinai, L.-S. Young and others, mathematical tools in the theory of hyperbolic and chaotic dynamical systems appear to be developed far enough to attack many open problems that have been so far only studied heuristically or numerically by physicists, if at all. In particular, we plan to investigate the nature of nonequilibrium steady states by means of Sinai-Ruelle-Bowen measures, time correlation functions that appear in transport laws and diffusion equations, open Hamiltonian systems that admit conditionally invariant measures, the motion of a massive particle in an ideal gas by using an appropriate space-time limit, etc. In each case we aim at obtaining exact results and providing solid rigorous proofs. The general goal of the project is to conduct mathematical studies of facts and phenomena that have attracted attention in physical community and have applications outside of mathematics. In particular, the results would contribute to the mathematical foundation of statistical mechanics and thermodynamics and could strengthen the link between the theory of dynamical systems and physics and other sciences.