Dynamics of a spin-boson model with structured spectral density

TL;DR

This paper investigates the dynamics of a two-state quantum system interacting with a structured environment, providing exact analytical expressions for bath correlations and population differences, and analyzing approximation validity.

Contribution

It introduces exact analytical formulas for bath correlation functions and population differences in a spin-boson model with structured spectral density, expanding understanding of system-environment interactions.

Findings

Derived an exact analytical expression for the bath correlation function.

Discussed the validity of various approximations based on system parameters.

Provided an exact expression for population difference within certain parameter ranges.

Abstract

We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various approximations to the correlation function for calculating the population difference of the system are discussed as function of tunneling splitting, oscillator frequency, coupling constant, damping rate and the temperature of the bath. An exact expression for the population difference for a limited range of parameters, is derived.