Nonperturbative approach to system-reservoir dynamics in the strong-coupling regime and non-Markovian dynamics

We present a method to derive an exact master equation for a bosonic system coupled to a set of other bosonic systems, which plays the role of the reservoir, under the strong-coupling regime, i.e., without resorting to either the rotating-wave or secular approximations. Working with phase-space distribution functions, we verify that the dynamics have two different behaviors. Considering that the initial state is a concentrated wave packet in phase space, we see that the center of this wave packet follows classical mechanics while its shape gets distorted. Moreover, we show that this distortion is caused by the counter-rotating terms as well as thermal fluctuations. Finally, we discuss conditions for non-Markovian dynamics.

Figure 1

Network of coupled quantum harmonic oscillators in a general topology.

Figure 2

The system of interest (represented by a single harmonic oscillator of the original network) interacting with the normal modes of the diagonalized reservoir (represented by the remaining oscillators of the network).