QUANTUM DISSIPATION AND COHERENCE

TL;DR

This paper explores the quantum description of dissipative systems, specifically the damped harmonic oscillator, revealing how irreversibility and quantum noise are represented through unitarily inequivalent states, coherent states, and algebraic deformations.

Contribution

It introduces a novel quantum framework for dissipative systems using unitarily inequivalent representations, coherent states, and q-deformed algebras, linking dissipation to quantum noise and irreversibility.

Findings

States split into unitarily inequivalent representations

Time evolution involves tunneling among these representations

Quantum noise relates to phase-space doubling

Abstract

We discuss dissipative systems in Quantum Field Theory by studying the canonical quantization of the damped harmonic oscillator (dho). We show that the set of states of the system splits into unitarily inequivalent representations of the canonical commutation relations. The irreversibility of time evolution is expressed as tunneling among the unitarily inequivalent representations. Canonical quantization is shown to lead to time dependent SU(1,1) coherent states. We derive the exact action for the dho from the path integral formulation of the quantum Brownian motion developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems is related to quantum noise effects. Finally, we express the time evolution generator of the dho in terms of operators of the $q$-deformation of the Weyl-Heisenberg algebra. The $q$-parameter acts as a label for the unitarily inequivalent representations.