  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 novel example where equilibration
emerges as a 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 equilibrated subsystems,
intra-entanglement 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.
