TY - GEN

T1 - On the approach to thermal equilibrium of macroscopic quantum systems

AU - Goldstein, Sheldon

AU - Tumulka, Roderich

PY - 2011

Y1 - 2011

N2 - In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghì [2, 3, 4], we considered an isolated, macroscopic quantum system. Let H be a micro-canonical "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 macro-state at energy E corresponds to a subspace Heq of H such that dimHeq/dimH is close to 1. We say that a system with state vector ψ ε H is in thermal equilibrium if ψ is "close" to Heq. We argue that for "typical" Hamiltonians, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.

AB - In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghì [2, 3, 4], we considered an isolated, macroscopic quantum system. Let H be a micro-canonical "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 macro-state at energy E corresponds to a subspace Heq of H such that dimHeq/dimH is close to 1. We say that a system with state vector ψ ε H is in thermal equilibrium if ψ is "close" to Heq. We argue that for "typical" Hamiltonians, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.

KW - approach to thermal equilibrium

KW - micro-canonical energy shell

KW - quantum statistical mechanics

KW - thermalization of closed macroscopic quantum systems

KW - typical Hamiltonian

KW - typical long-time behavior of quantum systems

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U2 - 10.1063/1.3577619

DO - 10.1063/1.3577619

M3 - Conference contribution

AN - SCOPUS:79955055047

SN - 9780735408876

T3 - AIP Conference Proceedings

SP - 155

EP - 163

BT - Non-Equilibrium Statistical Physics Today - Proceedings of the 11th Granada Seminar on Computational and Statistical Physics

T2 - 11th Granada Seminar on Computational and Statistical Physics

Y2 - 13 September 2010 through 17 September 2010

ER -