Emergence of Canonical Ensembles from Pure Quantum States

We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum state, the unitary dynamics of a generic weak interaction almost always drives the subsystem into the canonical ensemble, in the usual sense of typicality. A crucial step is taken by assuming that the matrix elements of the interaction Hamiltonian have random phases, while their amplitudes are left unrestricted.