Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 40, Issue 26, Pages F503-F509Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/40/26/F01
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This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand canonical density matrix involving a complete commuting set of observables including the Hamiltonian. The result obtained, which is derived for a generic finite-dimensional quantum system, shows that the equilibrium state arising from unitary evolution is always expressible in the canonical form, without the consideration of a system-bath decomposition.
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