Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model

Abstract

We study the dynamics of a classical disordered macroscopic model completely isolated frorn the environment reproducing, in a classical setting, the ‘quantum quench’ protocol. We show that, depending on the pre and post quench parameters, the systern approaches equilibrium, succeeding to act as a bath on itself, or remains out of equilibrium, in two different ways. In the latter one, the systern stays confined in a metastable state in which it undergoes stationary dynamics characterised by a single temperature. In the other, the systern ages and its dynamics are characterised by two temperaturas associated with observations rnade at short and long time differences (high and low frequencies). The parameter dependence of the asymptotic states is rationalised in terrns of a dynamic phase diagram with one equilibrium and two out of equilibrium phases. Aspects of pre-thermalisation are observed and discussed. Similarities and differences with the dynamics of the dissipative model are also explained.