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 $P\left(t\right)$ has been calculated to show that a finite bias may favor the short time coherence. The spectrum of the susceptibility ${\chi }^{″}\left(\omega \right)$ 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 $0<s\le 1$ by the condition of ${\chi }^{″}\left(\omega =0\right)=\infty$ when $\alpha ={\alpha }_c$. Finally, we show that Shiba’s relation is exactly satisfied in our results.

• Received 13 April 2009

DOI:https://doi.org/10.1103/PhysRevE.80.041106