Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

TL;DR

This paper derives new integrable nonlinear differential equations for non-stationary correlation functions in a one-dimensional Fermi gas, extending equilibrium models to non-equilibrium dynamics using Wick's theorem and hydrodynamics.

Contribution

It introduces a novel method to formulate integrable equations for out-of-equilibrium Fermi gases based solely on Wick's theorem and hydrodynamic principles.

Findings

Derived new nonlinear differential equations for non-equilibrium correlation functions.

Equations are integrable and generalize known equilibrium equations.

Provides tools for studying non-equilibrium electronic system dynamics.

Abstract

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium and provide vital tools to study non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form.