Quantum and classical dynamics of Langmuir wave packets

TL;DR

This paper derives a quantum Zakharov system in three dimensions, explores its reduction to a quantum vector NLS equation, and shows quantum effects prevent collapse and induce oscillations in Langmuir wave packets.

Contribution

It introduces a quantum Zakharov system with a Lagrangian structure and analyzes localized solutions, revealing quantum corrections' role in preventing collapse and causing oscillations.

Findings

Quantum corrections prevent collapse of Langmuir wave packets.

Quantum effects induce oscillatory behavior in wave packet width.

The variational method preserves conservation laws.

Abstract

The quantum Zakharov system in three-spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws are derived. In the adiabatic and semiclassical case, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schr\"odinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time-dependence of the Gaussian shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three-spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation.