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

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.