TY - JOUR

T1 - Approach to thermal equilibrium of macroscopic quantum systems

AU - Goldstein, Sheldon

AU - Lebowitz, Joel L.

AU - Mastrodonato, Christian

AU - Tumulka, Roderich

AU - Zanghi, Nino

PY - 2010/1/7

Y1 - 2010/1/7

N2 - 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+δE. The thermal equilibrium macrostate at energy E corresponds to a subspace Heq of H such that dim Heq /dimH is close to 1. We say that a system with state vector ψH is in thermal equilibrium if ψ is "close" to Heq. We show that for "typical" Hamiltonians with given eigenvalues, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This result is closely related to von Neumann's quantum ergodic theorem of 1929.

AB - 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+δE. The thermal equilibrium macrostate at energy E corresponds to a subspace Heq of H such that dim Heq /dimH is close to 1. We say that a system with state vector ψH is in thermal equilibrium if ψ is "close" to Heq. We show that for "typical" Hamiltonians with given eigenvalues, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This result is closely related to von Neumann's quantum ergodic theorem of 1929.

UR - http://www.scopus.com/inward/record.url?scp=76649136961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76649136961&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.81.011109

DO - 10.1103/PhysRevE.81.011109

M3 - Article

AN - SCOPUS:76649136961

SN - 1539-3755

VL - 81

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 1

M1 - 011109

ER -