On a random matrix model of quantum relaxation

In paper [8] two of us considered a two-level system interacting with a n-level reservoir with the system-reservoir interaction modeled by a random matrix. We presented there a formula for the expectation of the reduced density matrix of the system in the limit n --> infinity and discussed its properties and asymptotic forms in various regimes. In this paper we prove that the variance of of the reduced density matrix goes to zero as n --> infinity. We then give proofs for the formulas announced in [8] and discuss the long time behavior of the system.