  The dynamical behavior of quantum coherence of a displaced squeezed thermal
state in contact with an external bath is discussed in the present work. We use
a Fano-Anderson type of Hamiltonian to model the environment and solve the
quantum Langevin equation. From the solution of the quantum Langevin equation
we obtain the Green's functions which are used to calculate the expectation
value of the quadrature operators which are in turn used to construct the
covariance matrix. We use a relative entropy based measure to calculate the
quantum coherence of the mode. The single mode squeezed thermal state is
studied in the Ohmic, sub-Ohmic and the super-Ohmic limits for different values
of the mean photon number. In all these limits, we find that when the coupling
between the system and the environment is weak, the coherence decays
monotonically and exhibit a Markovian nature. When the system and the
environment are strongly coupled, we observe that the evolution is initially
Markovian and after some time it becomes non-Markovian. The non-Markovian
effect is due to the environmental back action on the system. Finally, we also
present the steady state dynamics of the coherence in the long time limit in
both low and high temperature regime. We find that the qualitative behavior
remains the same in both the low and high temperature limits. But quantitative
values differ because the coherence in the system is lower due to thermal
decoherence.
