Classical KMS condition and Tomita-Takesaki theory

DOI10.1007/BF01610495zbMath0323.28011OpenAlexW2906251670MaRDI QIDQ1224191

Mario Pulvirenti, Giovanni Gallavotti

Publication date: 1976

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01610495

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) General theory of von Neumann algebras (46L10) Miscellaneous applications of functional analysis (46N99)

Related Items

Unnamed Item ⋮ Poisson geometry ⋮ Essential self-adjointness of Liouville operator for 2D Euler point vortices ⋮ DLR-KMS correspondence on lattice spin systems ⋮ On one-parameter Koopman groups ⋮ Unbounded derivations and invariant trace states ⋮ KMS condition for stable states of infinite classical systems ⋮ Stability, equilibrium and KMS for an infinite classical system ⋮ Classical systems of infinitely many noninteracting particles ⋮ Operatore di Liouville e soluzioni statistiche delle equazioni di Hamilton ⋮ Selfadjointness of the Liouville operator for infinite classical systems ⋮ Unbounded derivations and invariant states ⋮ Integral representations of the classical KMS-states for quasifree evolutions ⋮ High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph ⋮ Algebraic characterization of ergodicity

Cites Work

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• Existence of ground states and KMS states for approximately inner dynamics
• Unbounded derivations of \(C^*\)-algebras
• Unbounded derivations
• Unbounded derivations in operator algebras
• On the equilibrium states in quantum statistical mechanics
• Statistical mechanics of quantum spin systems
• Tomita's theory of modular Hilbert algebras and its applications