Chaos and quantum thermalization

We show that a bounded, isolated quantum system of many particles in a initial state will approach thermal equilibrium if the energy which are superposed to form that state obey \ Berry's. Berry's conjecture is expected to hold only if the corresponding system is chaotic, and essentially states that the energy behave as if they were gaussian random variables. We review the evidence, and show that previously neglected effects substantially the case for Berry's conjecture. We study a rarefied hard-sphere gas an explicit example of a many-body system which is known to be classically, and show that an energy eigenstate which obeys Berry's conjecture a Maxwell--Boltzmann, Bose--Einstein, or Fermi--Dirac distribution for momentum of each constituent particle, depending on whether the wave are taken to be nonsymmetric, completely symmetric, or completely functions of the positions of the particles. We call this \ eigenstate thermalization. We show that a generic initial will approach thermal equilibrium at least as fast asO (\/\) t^-1, where \ is the uncertainty in the total energy the gas. This result holds for an individual initial state; in contrast to classical theory, no averaging over an ensemble of initial states is. We argue that these results constitute a new foundation for quantum mechanics.