Dynamical evolution of quantum oscillators toward equilibrium

A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem n << N of the global state approaches equilibrium. This provides a different example where stationarity emerges as natural phenomena under quantum dynamics alone, with no necessity to bring in any additional statistical postulates. Mixedness of equilibrated subsystems consisting of 1,2, ..., n << N clearly indicates that small subsystems are entangled with the rest of the state, i.e., the bath. Every single mode oscillator is found to relax in a mixed density matrix of the Boltzmann canonical form. In two oscillator stationary subsystems, intraentanglement within the "system" oscillators is found to exist when the magnitude of the squeezing parameter of the bath is comparable in magnitude with that of the coupling strength.