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arXiv · 0911.1724

On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems

Sheldon Goldstein·Joel L. Lebowitz·Christian Mastrodonato·Roderich Tumulka·Nino Zanghi
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Abstract

We consider 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 + delta E. The thermal equilibrium macro-state 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 in 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.

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Sheldon Goldstein, Joel L. Lebowitz, Christian Mastrodonato, Roderich Tumulka, Nino Zanghi. 2009-11-09. On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems. https://doi.org/10.1103/physreve.81.011109

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