1995/04/24 by M. Fannes, Reinhard F. Werner, Fannes, M. +2 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed Matter (cond-mat) #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #cond-mat #quant-ph
paper · pdf · doi:10.48550/arxiv.cond-mat/9504090
plain TeX, 26 pages, 5 figures in separate compressed .ps file. full postscript version from: ftp://ftp.physik.uni-osnabrueck.de/pub/werner/BoundaryConds/bcq.ps
arxiv created 1995/04/24 · openalex publication_date 1995/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem alone. The Hamiltonians for the subsystem are obtained by fixing a configuration for the variables in the complement of the subsystem, or more generally, by evaluating the full interaction Hamiltonian with respect to a state for the complement. We provide examples showing that the quantum mechanical version of this statement is false. It fails even if the subsystem is classical, but embedded into a quantum environment. We suggest an alternative characterization of the local restrictions of global equilibrium states by inequalities involving only local data.