Quantum Dissipation and Decay in Medium

TL;DR

This paper investigates quantum dissipation and decay processes in a thermal environment using path integrals, deriving the reduced density matrix for a harmonic oscillator coupled to a thermal bath, and analyzing the decay dynamics of unstable particles.

Contribution

It provides a general derivation of the reduced density matrix for harmonic oscillators with arbitrary bath spectra and elucidates the full decay process of unstable particles in thermal environments.

Findings

Unstable particles exhibit exponential decay followed by power-law decay.

Residual particles form a mixed state with contributions from on and off mass shell.

Abundance of residual particles is not suppressed by Boltzmann factors.

Abstract

Quantum dissipation in thermal environment is investigated, using the path integral approach. The reduced density matrix of the harmonic oscillator system coupled to thermal bath of oscillators is derived for arbitrary spectrum of bath oscillators. Time evolution and the end point of two-body decay of unstable particles is then elucidated: After early transient times unstable particles undergo the exponential decay, followed by the power law decay and finally ending in a mixed state of residual particles containing contributions from both on and off the mass shell, whose abundance does not suffer from the Boltzmann suppression.