W8. Thermalization of Nonintegrable Many-Body Systems

Workshop organized by:
S. Flach

Thermalization of Nonintegrable Many-Body Systems

We propose a topical workshop on the thermalization of nonintegrable many-body (macroscopic) systems. Dynamical Hamiltonian systems with macroscopic numbers of degrees of freedom at finite densities are assumed to be generically nonintegrable, thermalize (show ergodicity and mixing) and be far out of reach of the validity thresholds of the KAM regime of finite systems.
Recent results of Malishava and Flach (PRL 128 134102 2002) reveal that there are at least two distinct classes of weakly nonintegrable systems whose thermalization properties differ qualitatively. In one class, one-time scale diverges upon approaching the integrable limit and controls all other thermalization time scales. In the second class, an additional length scale is diverging upon approaching the integrable limit, making the class members ideal candidates for many-body localization upon subsequent quantization.
Results by Rumpf, Mithun and others showed that adding a second integral of motion to the existing energy one may lead to non-ergodic dynamics and non-Gibbs statistics even far from any integrable limit.
We want to merge the above communities and discuss recent advances in both directions. Among the many important questions, we propose to focus on the computing of critical exponents for the two system classes, the identifying of further novel system classes, the impact of disorder and quantization, the relaxing of the condition of having additional integrals of motion, among others.