Quantum-classical transition in dissipative systems through scaled trajectories

TL;DR

This paper introduces a nonlinear wave equation for dissipative quantum systems, demonstrating a smooth transition from quantum to classical behavior through scaled trajectories, and analyzing decoherence and localization effects.

Contribution

It proposes a new quantum-classical transition wave equation and demonstrates its equivalence to a scaled Schrödinger equation, enabling visualization of decoherence and localization.

Findings

Smooth transition from Bohmian to classical trajectories

Visualization of decoherence and localization processes

Analysis of Gaussian wave packet propagation in dissipative media

Abstract

A nonlinear quantum-classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schr\"{o}dinger equation is proved. The dissipative dynamics is then studied in terms of what we call scaled trajectories following the standard procedure used in Bohmian mechanics. These trajectories depend on a continuous parameter allowing us a smooth transition from Bohmian to classical trajectories. Arrival times and actual momentum distribution functions are also analyzed. The propagation of a Gaussian wave packet in a viscid medium under the presence of constant, linear and harmonic potentials is studied. The gradual decoherence process and localization are easily visualized and understood within this theoretical framework.