Non-Markovian dynamics for bipartite systems

TL;DR

This paper investigates non-Markovian effects in bipartite quantum systems, deriving a new quantum master equation that captures complex decoherence behaviors like stretched exponential decay.

Contribution

It introduces the quantum Bloch-Boltzmann equation, a novel master equation for bipartite systems with non-Markovian dynamics, bridging motional and internal states.

Findings

Non-Markovian effects lead to stretched exponential and power-law decay of coherences.

The derived equation models both motional and internal degrees of freedom.

Classical treatment of one subsystem reveals non-Markovian decoherence behaviors.

Abstract

We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which we term quantum Bloch-Boltzmann equation, is derived, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom is amenable to a classical treatment and not resolved in the final measurement, though relevant for the interaction with the reservoir, non-Markovian behaviors such as stretched exponential or power law decay of coherences can be put into evidence.