
doi: 10.1007/bf01617992
We demonstrate, under circumstances that allow the construction of a “thermodynamic” hamiltonian, that Gibbs equilibrium states ω are modular states in the Tomita-Takesaki sense. The thermodynamic Greens functionsG are connected to these modular states, and the associated group of modular automorphisms σ, by the identification $$G(A, B; t) = \omega (A\sigma _t (B))$$ (A andB are observables) whenever the thermodynamic Hamiltonian is self-adjoint and defines a derivation of the algebra of observables in a certain sense. Our results apply to a class of interacting quantum gases at small fugacity and Bose gases with repulsive interactions at all fugacitiesz<1.
Miscellaneous applications of functional analysis, 46L05, General theory of von Neumann algebras, 82.46
Miscellaneous applications of functional analysis, 46L05, General theory of von Neumann algebras, 82.46
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 20 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
