Ehrenfest breakdown of the mean-field dynamics of Bose gases

TL;DR

This paper demonstrates that the mean-field dynamics of Bose gases break down at a logarithmic time scale related to the Ehrenfest time, which can be experimentally observed in Bose-Einstein condensates.

Contribution

It introduces a formalism in particle-number phase space to describe the Ehrenfest breakdown of mean-field dynamics in Bose gases, linking it to quantum fidelity and Lyapunov exponents.

Findings

Breakdown time scales logarithmically with particle number N.

The breakdown is characterized by quantum fidelity of reduced density matrices.

Results are illustrated with a triple-well Bose gas model.

Abstract

The mean-field dynamics of a Bose gas is shown to break down at time $\tau_h = (c_1/\gamma) \ln N$ where $\gamma$ is the Lyapunov exponent of the mean-field theory, $N$ is the number of bosons, and $c_1$ is a system-dependent constant. The breakdown time $\tau_h$ is essentially the Ehrenfest time that characterizes the breakdown of the correspondence between classical and quantum dynamics. This breakdown can be well described by the quantum fidelity defined for reduced density matrices. Our results are obtained with the formalism in particle-number phase space and are illustrated with a triple-well model. The logarithmic quantum-classical correspondence time may be verified experimentally with Bose-Einstein condensates.