Mean field evolution in an open quantum system

Abstract

In this thesis, we consider N quantum particles coupled to collective thermal quantum environments. The coupling is energy conserving and scaled in the mean field way. There is no direct interaction between the particles, they only interact via the common reservoir. It is well known that an initially disentangled state of the N particles will remain disentangled at times in the limit N -> [infinity]. In this thesis, we evaluate the η-body reduced density matrix (tracing over the reservoirs and the N - η remaining particles). We identify the main disentangled part of the reduced density matrix and obtain the first order correction term in 1/N. We show that this correction term is entangled. We also estimate the speed of convergence of the reduced density matrix as N -> [infinity]. Our model is exactly solvable and it is not based on numerical approximation.