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 ${\alpha }_c=\frac{1}{2}[1+{\Delta }_r/{\omega }_c]$; 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 $C(t)\approx -1/{\gamma }_c^2{t}^2$ in the long time limit.

9 pages, 2 figures