  The quantum dynamics of a two-level system coupled to an Ohmic spin- bath is
studied by means of the perturbation approach based on a unitary
transformation. A scattering function $\xi_k$ is introduced in the
transformation to take into account quantum fluctuations. By the master
equation within the Born approximation, nonequilibrium dynamics quantities are
calculated. The method works well for the coupling constant $0 < \alpha <
\alpha_c$ and a finite bare tunneling $\Delta$. It is found that (i) only at
zero temperature with small coupling or moderate one does the spin-spin-bath
model display identical behavior as the well known spin-boson-bath model; (ii)
in comparison with the known results of spin-boson-bath model, the
coherence-incoherence transition point, which occurs at
$\alpha_c={1/2}[1+\eta\Delta/\omega_c]$, is temperature independent; (iii) the
nonequilibrium correlation function $P(t)=<\tau_z(t)>$, evolves without
temperature dependence while $<\tau_x(t)>$ depends on temperature. Both $P(t)$
and $<\tau_x(t)>$ not only satisfy their initial conditions, respectively, and
also have correct long time limits. Besides, the Shiba's relation and sum rule
are exactly satisfied in the coherent regime for this method. Our results show
that increasing temperature does not help the system suppress decoherence in
the coherent regime, i.e., finite temperature does not favor the coherent
dynamics in this regime. Thus, the finite-temperature dynamics induced by two
kinds of baths spin-bath and boson-bath exhibit distinctly different physics.
