Decay process of quantum open system at finite-temperature

TL;DR

This paper analyzes the decay dynamics of a quantum harmonic oscillator coupled to a boson bath at finite temperature, revealing how initial states evolve and how temperature influences decay processes.

Contribution

It introduces a method based on the Heisenberg equation solution to study decay in quantum open systems at finite temperature, providing new insights into state evolution and effective Hamiltonians.

Findings

Initial coherent states evolve into temperature-dependent coherent states.

A temperature-dependent effective Hamiltonian characterizes short-time decay.

The method effectively analyzes decay processes for Fock and coherent states.

Abstract

Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a coherent state demonstrate that this method is very useful in dealing with the problems in decay process of the open system. For finite temperature, the calculations of the reduced density matrix and the mean excitation number for the open system show that an initial coherent state will evolve into a temperature-dependant coherent state after tracing over the bath variables. Also in short-time limit, a temperature-dependant effective Hamiltonian for the open system characterizes the decay process of the open system.