Dynamics of a Two-Level System Coupled to Ohmic Bath: A Perturbation Approach

TL;DR

This paper investigates the dynamics of a two-level quantum system coupled to an Ohmic bath using a perturbation method, revealing a coherence-incoherence transition and detailed spectral properties.

Contribution

It introduces a perturbation approach based on a unitary transformation to analyze the system's dynamics and precisely characterizes the coherence transition point.

Findings

Coherence-incoherence transition at α_c = 0.5(1 + Δ_r/ω_c)

Dynamical quantity P(t) = cos(ω_0 t) exp(-γ t) for α<α_c

Double peak structure in susceptibility χ''(ω)/ω for α<α_c

Abstract

The physics of a two-level system coupled to Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. Our main results are: The coherence-incoherence transition is at $\alpha_c={1\over 2}[1+\Delta_r/\omega_c]$; for $\alpha<\alpha_c$ the dynamical quantity $P(t)=\cos(\omega_0 t)\exp(-\gamma t)$; the sussceptibility $\chi^{\prime\prime}(\omega)/\omega$ is of a double peak structure for $\alpha<\alpha_c$ and the Shiba's relation is exactly satisfied; at the transition point $\alpha=\alpha_c$ the real time correlation function $C(t)\approx -1/\gamma^2_c t^2$ in the long time limit.