Integrability as an attractor of adiabatic flows

Abstract

Generic many-body particle systems typically exhibit chaos and thermalization. Amidst this chaotic landscape there are special systems called integrable, for example, systems of noninteracting particles that are neither chaotic nor thermalizing. Integrable systems usually require a high degree of fine-tuning of the Hamiltonian that defines their dynamics. The authors find that these special systems act as natural geometric attractors of adiabatic flows that follow the directions of fastest relaxation of observables. They also found that near integrability observables exhibit universal slow relaxation in time, forming long-lived nonequilibrium states similar to turbulent cascades.

Topics & Concepts