Thermalization dynamics of macroscopic weakly nonintegrable maps

Abstract

We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity, the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices, the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance [Formula: see text] of finite time average distributions for extended and local observables. We extract the ergodization time scale [Formula: see text] which marks the onset of thermalization, and determine the type of network through the subsequent decay of [Formula: see text]. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time [Formula: see text] with [Formula: see text]. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.