Phase-space stochastic quantum hydrodynamics for interacting Bose gases

Hydrodynamic theories offer successful approaches that are capable of simulating the otherwise difficult-tocompute dynamics of quantum many-body systems. In this work we derive, within the positive-P phase-space formalism, a 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 nonequilibrium quantum correlations, even for short-wavelength phenomena. Using this description, we derive a linearized stochastic hydrodynamic scheme which is able to simulate such nonequilibrium 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.

Automated summary

This paper presents a stochastic hydrodynamic method in the positive-P phase-space formalism, which can simulate the full quantum dynamics of interacting Bose gases and compute nonequilibrium quantum correlations. A linearized stochastic hydrodynamic scheme is also derived, which can simulate non-equilibrium situations for a longer time.