Phase-space stochastic quantum hydrodynamics for interacting Bose gases

TL;DR

This paper introduces a novel stochastic hydrodynamic method within the positive-P phase-space formalism for simulating the full quantum dynamics of interacting Bose gases, including non-equilibrium correlations and short-wavelength phenomena.

Contribution

It develops a new phase-space stochastic hydrodynamic approach that surpasses existing methods in capturing quantum correlations in Bose gases, with a linearized scheme for longer-time simulations.

Findings

Successfully simulates quantum shock wave correlations.

Shows agreement with established quantum many-body approaches.

Extends simulation capabilities to non-equilibrium, short-wavelength phenomena.

Abstract

Hydrodynamic theories offer successful approaches that are capable of simulating the otherwise difficult-to-compute dynamics of quantum many-body systems. In this work we derive, within the positive-P phase-space formalism, a new stochastic hydrodynamic method for the description of interacting Bose gases. It goes beyond existing hydrodynamic approaches, such as superfluid hydrodynamics or generalized hydrodynamics, in its capacity to simulate the full quantum dynamics of these systems: it possesses the ability to compute non-equilibrium quantum correlations, even for short-wavelength phenomena. Using this description, we derive a linearized stochastic hydrodynamic scheme which is able to simulate such non-equilibrium situations for longer times than the full positive-P approach, at the expense of approximating the treatment of quantum fluctuations, and show that this linearized scheme can be directly connected with existing Bogoliubov approaches. Furthermore, we go on to demonstrate the usefulness and advantages of this formalism by exploring the correlations that arise in a quantum shock wave scenario and comparing its predictions to other established quantum many-body approaches.