Quantum corrections to nonlinear ion acoustic wave with Landau damping

TL;DR

This paper derives a quantum-corrected higher-order KdV equation for nonlinear ion acoustic waves with Landau damping, showing slow amplitude decay influenced by quantum effects.

Contribution

It introduces a quantum correction to the classical nonlinear ion acoustic wave equation, incorporating higher-order nonlinear terms and quantum Landau damping effects.

Findings

Quantum corrections lead to a higher-order KdV equation.

Amplitude decay is slow and influenced by quantum parameter Q.

Total ion number conservation is demonstrated.

Abstract

Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to presence of Landau damping terms has been calculated assuming the Landau damping parameter $\alpha_1 = \sqrt{{m_e}/{m_i}}$ to be of the same order of the quantum parameter $Q = {\hbar^2}/({24 m^2 c^2_{s} L^2})$. The amplitude is shown to decay very slowly with time as determined by the quantum factor $ Q$.