On spatial decoherence in many-body systems

Abstract

We study the dynamics of a many-body quantum system strongly interacting with a bosonic reservoir. The coupling is given by a potential operator for the system and it is linear in the field. We show that in the limit of infinite coupling strength the system undergoes instantaneous spatial decoherence. To resolve the decoherence process in time we consider large coupling strengths $\lambda$ and short times scaling as $t\propto \lambda^{-\alpha}$, with $\alpha\ge0$, in the limit $\lambda\rightarrow\infty$. On short time scales $\alpha>1$ the dynamics is trivial while on longer ones $0\le\alpha<1$ the decoherence is instantaneous. We show that the decoherence process is resolved exactly for $\alpha=1$, defining the fine-grained time scale $\tau=\lambda t$. We construct an approximate effective evolution map of the many-body system with controlled error estimates. Generically, the effective dynamics is markovian, but not given by a dynamical semigroup. As a physical application we give a rigorous description of the phenomenon of localization of macroscopic quantum objects in position space.