Energy-space random walk in a driven disordered Bose gas

TL;DR

This paper investigates the energy growth dynamics of a driven disordered Bose gas, revealing a crossover between two scaling regimes through numerical simulations and a semi-classical energy-space random walk model.

Contribution

It introduces a semi-classical model explaining the energy growth crossover in a driven disordered Bose gas, supported by numerical Schrödinger-equation simulations.

Findings

Energy growth follows a power-law with exponent ~0.5 at weak disorder.

A crossover to an exponent ~0.4 occurs with increasing disorder.

The model predicts a transition from energy growth limited by scattering to drive-induced energy change.

Abstract

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, $E \propto t^{\eta}$ with $\eta=0.46(2)$, and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schr\"odinger-equation simulations reveal a crossover from $\eta \approx 0.5$ to $\eta \approx 0.4$ 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.