  A new analytical approach, beyond rotating wave approximation, based on
unitary transformations and the non-Markovian master equation for the density
operator, is applied to treat the biased spin boson model with a Lorentzian
structured bath for arbitrary detunings at zero temperature. Compared to zero
bias, we find that the dynamics demonstrates two more damping oscillation
frequencies and one additional relaxation frequency for non-zero bias, where
one of the damping oscillation frequencies is a new effect. Analytical
expressions for the non-Markovian dynamics and the corresponding spectrum, the
localized-delocalized transition point, the coherent-incoherent transition
point, the analytical ground energy, the renormalized tunneling factor and the
susceptibility are determined. The sum rule and the Shiba relation are checked
in the coherent regime.
