Thermalization of an Oscillating Bose Condensate in a Disordered Trap

Abstract

Previously, we numerically showed that thermalization can occur in an oscillating Bose–Einstein condensate with a disordered harmonic trap when the healing length $\xi$ of the condensate is shorter than the correlation length $\sigma _{D}$ of the Gaussian disorder [see, for example, the experiment reported in Dries et al. (Phys Rev A 82:033603, 2010)]. In this work, we investigate and show that in the $\xi >\sigma _{D}$ (Anderson localization) regime, the system can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle number are conserved and the irreversible evolution toward thermodynamic equilibrium is induced by the disorder. The thermodynamic equilibrium is evidenced by the maximized entropy $S\left[ n_{k}\right]$ in which the waveaction spectrum $n_{k}$ follows the Rayleigh–Jeans distribution. Besides, unlike a monotonic irreversible process of thermalization to equilibrium, the Fermi–Pasta–Ulam–Tsingou recurrence arises in this system, manifested by the oscillation of the nonequilibrium entropy.