Quantum detailed balance. (English) Zbl 0581.46065
This paper considers quantum systems. First a family of dissipative maps satisfying the detailed balance condition (DBC) is build for infinite quantum systems (DBC means reversibility). For finite systems DBC provides a characterization of the equilibrium states.
Then considering closed systems the authors conjecture that every state left invariant under the set of dissipative maps satisfying DBC is an equilibrium state. The conjecture is proved for finite systems and for the infinite free Fermion gas.
Then considering closed systems the authors conjecture that every state left invariant under the set of dissipative maps satisfying DBC is an equilibrium state. The conjecture is proved for finite systems and for the infinite free Fermion gas.
Reviewer: P.Hillion
MSC:
| 46N99 | Miscellaneous applications of functional analysis |
| 82B30 | Statistical thermodynamics |
| 81Q99 | General mathematical topics and methods in quantum theory |
Keywords:
family of dissipative maps; detailed balance condition; infinite quantum systems; characterization of the equilibrium states; closed systems; infinite free Fermion gasReferences:
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