Abstract
We consider an isolated macroscopic quantum system. Let be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between and . The thermal equilibrium macrostate at energy corresponds to a subspace of such that is close to 1. We say that a system with state vector is in thermal equilibrium if is “close” to . We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors evolve in such a way that is in thermal equilibrium for most times . This result is closely related to von Neumann’s quantum ergodic theorem of 1929.
- Received 9 November 2009
DOI:https://doi.org/10.1103/PhysRevE.81.011109
©2010 American Physical Society