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

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) = 1/2[1 + Delta(r)/omega(c)]; for alpha < α(c) the non-equilibrium correlation P(t) = cos(ω(0)t) exp(-γt); the susceptibility χ&DPRIME;(ω)/ω is of a double peak structure for α &LT; α(c) and the Shiba's relation is exactly satisfied; at the transition point α = α(c) the equilibrium correlation C(t) ≈ -1/γ(2)(c)t(2) in the long time limit.