Dissipation evidence for the quantum damped harmonic oscillator via pseudo-bosons

TL;DR

This paper investigates the quantum damped harmonic oscillator and finds that the associated vacua are non square-integrable, providing quantum-level evidence of dissipation effects in the system.

Contribution

It demonstrates that the vacua linked to the quantum damped harmonic oscillator are non square-integrable when expressed via pseudo-bosonic operators, highlighting dissipation at the quantum level.

Findings

Vacua are non square-integrable in the pseudo-bosonic framework

Evidence of dissipation at the quantum level

Supports classical dissipation with quantum signatures

Abstract

It is known that a self-adjoint, time-independent hamiltonian can be defined for the quantum damped harmonic oscillator. We show here that the two vacua naturally associated to this operator, when expressed in terms of pseudo-bosonic lowering and raising operators, appear to be non square-integrable. This fact is interpreted as the evidence of the dissipation effect of the classical oscillator at a purely quantum level.