Energy-space random walk in a driven disordered Bose gas

Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, E propto t^η with η=0.46(2), and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from ηapprox 0.5 to ηapprox 0.4 with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from E propto t^1/2 to E propto t^2/5 scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system's energy. Our results provide the theoretical foundation for further experiments.