Derivation of a two-fluids model for a Bose gas from a quantum kinetic system

TL;DR

This paper derives a two-fluids hydrodynamic model for a Bose gas with condensation from quantum kinetic equations, analyzes its properties, and provides numerical examples to illustrate the model.

Contribution

It introduces a formal derivation of a two-fluids Euler system from a quantum kinetic framework for Bose gases with condensation, including analysis of hyperbolicity and weak solutions.

Findings

Conditions for hyperbolicity identified

Weak solutions analyzed

Numerical example demonstrated

Abstract

We formally derive the hydrodynamic limit of a system modelling a bosons gas having a condensed part, made of a quantum kinetic and a Gross-Pitaevskii equation. The limit model, which is a two-fluids Euler system, is approximated by an isentropic system, which is then studied. We find in particular some conditions for the hyperbolicity, and we study the weak solutions. A numerical example is given at the end.