Abstract
Standard textbook always starts its discussion of quantum statistical mechanics with the microcanonical ensemble, which is established by postulates. We show that these postulates are not necessary; one can establish microcanonical ensemble directly from the Schroedinger equation without any postulate. We find that an isolated quantum chaotic system in a pure state in general can equilibrate and serve as a heat bath (or microcanonical ensemble). Once the equilibrium is reached, any of its subsystems that is much smaller than the isolated system is thermalized so that the subsystem is governed by the Gibbs distribution. Within our theoretical framework, the celebrated superposition principle of quantum mechanics should lead to a prediction of a thermalized subsystem with multiple temperatures if the isolated system is in a superposition state of energy eigenstates of multiple distinct energy scales. This multiple temperature state is at equilibrium, completely different from a non-equilibrium state that has multiple temperatures at different parts.
Coffee and tea will be served 20 minutes prior to the seminar.