title: Approach to thermal equilibrium of macroscopic quantum systems.
abstract: We consider an isolated macroscopic quantum system. Let H 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 E and E+deltaE . The thermal equilibrium macrostate at energy E corresponds to a subspace H(eq) of H such that dim H(eq)/dim H is close to 1. We say that a system with state vector psi is the element of H is in thermal equilibrium if psi is "close" to H(eq). We show that for "typical" Hamiltonians with given eigenvalues, all initial state vectors psi(0) evolve in such a way that psi(t) is in thermal equilibrium for most times t. This result is closely related to von Neumann's quantum ergodic theorem of 1929.
authors.affiliation: Departments of Mathematics and Physics, Rutgers University, Piscataway, New Jersey 08854-8019, USA. oldstein@math.rutgers.edu
authors.forename: Sheldon
authors.initials: S
authors.lastname: Goldstein
authors.forename: Joel L
authors.initials: JL
authors.lastname: Lebowitz
authors.forename: Christian
authors.initials: C
authors.lastname: Mastrodonato
authors.forename: Roderich
authors.initials: R
authors.lastname: Tumulka
authors.forename: Nino
authors.initials: N
authors.lastname: Zanghi