Search results for "Gibbs states"

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A Note on States and Traces from Biorthogonal Sets

2019

In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L &dagger

Pure mathematicsnon-Hermitian HamiltoniansGibbs statePhysics and Astronomy (miscellaneous)lcsh:MathematicsGeneral Mathematicsbiorthogonal sets of vector010102 general mathematicsGibbs stateslcsh:QA1-93901 natural sciencesDomain (software engineering)TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSettore MAT/05 - Analisi MatematicaChemistry (miscellaneous)Biorthogonal system0103 physical sciencesComputer Science (miscellaneous)0101 mathematics010306 general physicsMathematicsSymmetry
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Gibbs states, algebraic dynamics and generalized Riesz systems

2020

In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita-Takesaki theory in our context.

Pure mathematicsPhysical systemFOS: Physical sciencesBiorthogonal sets of vectors01 natural sciencesUnitary statesymbols.namesakeSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: MathematicsOrthonormal basis0101 mathematicsAlgebraic numberOperator Algebras (math.OA)Eigenvalues and eigenvectorsMathematical PhysicsMathematics010308 nuclear & particles physicsMathematics::Operator AlgebrasApplied Mathematics010102 general mathematicsTime evolutionMathematics - Operator AlgebrasTomita–Takesaki theoryMathematical Physics (math-ph)Gibbs statesNon-Hermitian HamiltoniansComputational MathematicsComputational Theory and MathematicsBiorthogonal systemsymbolsHamiltonian (quantum mechanics)
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