Non-Markovian dynamics of a dissipative two-level system: nonzero bias and sub-Ohmic bath.

The quantum dynamics of the dissipative two-level system with nonzero bias and sub-Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. It has been shown that for the sub-Ohmic bath it is necessary to use the non-Markovian approach, especially for the short time behavior of the coupled system and environment. The nonequilibrium correlation P(t) has been calculated to show that a finite bias may favor the short time coherence. The spectrum of the susceptibility chi"(omega) of the sub-Ohmic case may have a double peak structure in the range of omega>0 when the coupling alpha is relatively strong. Besides, the coherence-decoherence transition point alpha(c) is determined for different 0<s<or=1 by the condition of chi''(omega=0)=infinity when alpha=alpha(c). Finally, we show that Shiba's relation is exactly satisfied in our results.