Quantum Particle Motion in Absorbing Harmonic Trap

TL;DR

This paper investigates quantum energy dissipation in a damped harmonic oscillator using Feynman path integrals, revealing how complex potentials model energy loss and irreversibility at the quantum level.

Contribution

It introduces a novel approach to analyze quantum damping via complex harmonic potentials within the path integral framework, expanding understanding of quantum irreversibility.

Findings

Energy loss modeled by complex harmonic potential

Damped wave function lacks probability interpretation

Quantified energy dissipation and irreversibility

Abstract

The motivation of this work is to get an additional insight into the irreversible energy dissipation on the quantum level. The presented examination procedure is based on the Feynman path integral method that is applied and widened towards the calculation of the kernel of a quantum mechanical damped oscillator. Here, it is shown that the energy loss of the oscillator can be generated by the introduced harmonic complex potential. The related damped wave function, however, does not pertain to the probability meaning as it is usual in the case of complex absorbing potentials. This decrease of the wave function is evaluated, moreover, the energy dissipation and the measure the irreversibility are expressed.