Quantum systems coupled to environments via mean field interactions

Abstract

We show that when a quantum system is coupled to an environment in a mean field way, then its effective dynamics is governed by a unitary group with a time-dependent Hamiltonian. The time-dependent modification of the bare system Hamiltonian is given by an explicit term involving the reservoir state. We show that entanglement within the system state is not changed during the dynamics. Our results hold for arbitrary strengths of the system-environment coupling, and for finite or infinite dimensional systems. As an application we show that the qualitative dynamical features of an $N$-body system can be altered drastically by the contact with the environment. For instance, a system having bound states only (point spectrum) can turn into a system with only scattering states (continuous spectrum) and vice-versa.