Kinetic theory for oscillator chains

Mathphys Analysis Seminar

A chain of oscillators is a Hamiltonian model set on the 1D lattice (Z), which should be thought as a model of a crystal: particles can interact with their neighbors, linearly and nonlinearly. The most prominent examples are the Fermi-Pasta-Ulam and the Toda equations. I will present the kinetic (Boltzmann-type) equation which can be derived from this model as well as its hydrodynamic limits. I will try to give an overview of the - mostly not rigorous - theory, but also emphasize recent mathematical progress.