2007/02/28 by Dorje C Brody, Dorje C. Brody, Daniel W. Hook +3 · 18 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Density matrix #Ergodic theory #Ergodicity #Linear subspace #Observable #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Quantum state #Quantum system #State (computer science) #Stationary ergodic process #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/26/f01
published in Journal of Physics A Mathematical and Theoretical 40(26), F503-F509 (Institute of Physics) · 8 pages
openalex publication_date 2007/06/12 · arxiv created 2007/06/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.