A New Cumulant Expansion Based Extraction for Higher Order Quantum Corrections in Equilibrium Wigner-Boltzmann Equation

TL;DR

This paper introduces a cumulant expansion method for efficiently extracting higher-order quantum corrections in the equilibrium Wigner-Boltzmann equation, offering faster convergence than traditional moment expansion especially near Maxwellian distributions.

Contribution

It presents a novel cumulant-based approach that converges faster than moment expansion for quantum correction extraction in equilibrium distributions.

Findings

Cumulant expansion converges faster than moment expansion near Maxwellian distributions.

Higher-order quantum corrections can be obtained using only the first three cumulants.

The method offers a new way to analyze the role of potential functions in quantum corrections.

Abstract

A Cumulant based method has been introduced to extract quantum corrections in distribution function with the equilibrium Wigner-Boltzmann equation. It is shown that unlike the moment expansion used in hydrodynamic model, cumulant expansion converges much faster when distribution function is closed to Maxwellian with only first three cumulants are non-zero. In this case, quantum corrections higher than first order can be extracted mainly by lowest three cumulants and odd number derivatives of potential function. This method also provides a new way to determine the distribution function with Maxwellian form and study the role of potential function in quantum correction field.