Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

Abstract.

The quantum dynamics, both non-equilibrium and equilibrium, of the dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. It works well for the whole parameter range $0 < \alpha < 1$ and $0 < \Delta < \omega_c$ and 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 non-equilibrium correlation $P(t) = \cos(\omega_0 t)\exp(-\gamma t)$; the susceptibility $\chi^{\prime\prime}(\omega)/\omega$ 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 equilibrium correlation $C(t)\approx -1/\gamma^2_c t^2$ in the long time limit.