Details
| Original language | English |
|---|---|
| Pages (from-to) | 635-657 |
| Number of pages | 23 |
| Journal | Helv. Phys. Acta |
| Volume | 68 |
| Issue number | 7-8 |
| Publication status | Published - 1995 |
Abstract
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In: Helv. Phys. Acta, Vol. 68, No. 7-8, 1995, p. 635-657.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Boundary conditions for quantum lattice systems
AU - Fannes, M.
AU - Werner, R. F.
PY - 1995
Y1 - 1995
N2 - 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.
AB - 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.
M3 - Article
VL - 68
SP - 635
EP - 657
JO - Helv. Phys. Acta
JF - Helv. Phys. Acta
IS - 7-8
ER -