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

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 $α_c={1\over 2}[1+Δ_r/ω_c]$; for $α<α_c$ the dynamical quantity $P(t)=\cos(ω_0 t)\exp(-γt)$; the sussceptibility $χ^{\prime\prime}(ω)/ω$ is of a double peak structure for $α<α_c$ and the Shiba&#39;s relation is exactly satisfied; at the transition point $α=α_c$ the real time correlation function $C(t)\approx -1/γ^2_c t^2$ in the long time limit.