Exact Density matrix of an oscillator-bath system: Alternative derivation

TL;DR

This paper presents a new derivation of the exact quantum propagator and density matrix for an oscillator-bath system, including cases with external forces, providing precise analytical tools for quantum open systems.

Contribution

It introduces a novel derivation method for the exact quantum propagator and density matrix of an oscillator-bath system, extending to external force influences.

Findings

Exact density matrix derived from the quantum propagator

Reduced density matrix of the main oscillator obtained

Generalized propagator for systems with external classical forces

Abstract

Starting from a total Lagrangian describing an oscillator-bath system, a novel derivation of exact quantum propagator is presented. Having the quantum propagator, the exact density matrix, reduced density matrix of the main oscillator and thermal equilibrium fixed point are obtained. The problem is generalised to the cases where the main oscillator is under the influence of a classical external force. By introducing generalised auxiliary classical fields, the generalised quantum propagator or generating functional of position correlation functions is obtained.