6533b871fe1ef96bd12d1b8d

RESEARCH PRODUCT

Gibbs states, algebraic dynamics and generalized Riesz systems

Camillo TrapaniHiroshi InoueFabio Bagarello

subject

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)

description

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.

yearjournalcountryeditionlanguage
2020-09-07
http://arxiv.org/abs/2009.02950