Thermalization of Quantum States

An exact stochastic model for the thermalization of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterized by an underlying Schrödinger evolution, together with a nonlinear term driving the system toward an asymptotic equilibrium state and a stochastic term reflecting fluctuations. There are two free parameters, one of which can be identified with the heat bath temperature, while the other determines the characteristic time scale for thermalization. Exact expressions are derived for the evolutionary dynamics of the system energy, the system entropy, and the associated density operator