Quantum systems coupled to environments via mean field interactions

TL;DR

This paper demonstrates that quantum systems coupled to environments via mean field interactions evolve under a time-dependent Hamiltonian, with entanglement unaffected, and environmental contact can significantly alter system dynamics.

Contribution

It provides an explicit form for the effective dynamics of quantum systems under mean field environmental coupling, applicable to various system sizes and coupling strengths.

Findings

Entanglement remains unchanged during mean field dynamics.

Environmental contact can transform bound states into scattering states.

Effective dynamics are governed by a time-dependent Hamiltonian.

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, bound states can turn into scattering states and vice-versa.