Dynamical typicality: Convergence of time evolved macro-observables to their mean values in random matrix models

Abstract

Here we analyze the notion of dynamical typicality in large quantum random matrix models. By dynamical typicality we mean that different Hamiltonian systems evolve in time in a practically indistinguishable manner. We prove dynamical typicality for a Hamiltonian belonging to the Gaussian unitary ensemble (GUE) ensemble and argue in the conclusion why the same result is valid for more general Hamiltonians.