Hydrodynamics for quasi-free quantum systems

TL;DR

This paper derives hydrodynamic equations for quasi-free quantum systems using Wigner functions, extending to band distributions, and analyzes fluctuations in Bosonic hard rods, contributing to understanding quantum fluid dynamics.

Contribution

It introduces a hydrodynamic derivation for quasi-free quantum systems and extends the framework to include band distributions and fluctuation analysis.

Findings

Derived Euler equations for quantum systems using hydrodynamic limit

Extended distribution functions to particles in periodic potentials

Calculated density fluctuations in Bosonic hard rods

Abstract

We consider quasi-free quantum systems and we derive the Euler equation using the so-called hydrodynamic limit. We use Wigner's well-known distribution function and discuss an extension to band distribution functions for particles in a periodic potential. We investigate the Bosonic system of hard rods and calculate fluctuations of the density. Keywords: Euler equation, quantum distribution function, hydrodynamic limit