Self-consistent fluid model for a quantum electron gas

TL;DR

This paper introduces a self-consistent fluid model that simplifies the Wigner-Poisson system to an effective nonlinear Schrödinger-Poisson system, accurately capturing quantum electron gas behavior and phenomena like stationary states and two-stream instability.

Contribution

It derives a novel nonlinear Schrödinger-Poisson model from the Wigner-Poisson system for quantum electron gases, applicable to various statistical mixtures.

Findings

Effective Schrödinger-Poisson system matches Wigner-Poisson results in long wavelength limit.

The model describes stationary states of quantum electron gases.

It captures the two-stream instability in quantum plasmas.

Abstract

It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of a zero-temperature one-dimensional electron gas, this additional nonlinearity is of the form Psi^4. In the long wavelength limit, the results obtained from the effective Schroedinger-Poisson system are in agreement with those of the Wigner-Poisson system. The reduced model is further used to describe the stationary states of a quantum electron gas and the two-stream instability.