Coherence and a quench dynamics of a dissipative quantum system: renormalization group and dynamical phases

We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subjected to an abrupt quench in the parameters of the underlying Hamiltonian was investigated using two complementary renormalization group approaches. The methods were applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory and the spin-boson coupling strength in the pre- and post-quench behavior is investigated. Additionally, we revealed several ``phases'' of the relaxation dynamics distinguished by the discrimination of the damping at long and intermediate time scale. Surprisingly, elevated temperature can render the system ``more coherent'' by inducing a transition from the partially coherent to the coherent regime.