Phase-space mixing in dynamically unstable, integrable few-mode quantum systems

Abstract

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as $1/O(\ln N)$, where $N$ is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

17 pages, 9 figures

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• Thermalization and its Breakdown for a Large Nonlinear Spin
• Coherent seeding of the dynamics of a spinor Bose-Einstein condensate: from quantum to classical behavior
• Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model
• How to probe the microscopic onset of irreversibility with ultracold atoms
• A semiclassical theory of phase-space dynamics of interacting bosons