In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyze two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy operator: we first consider those operators which are simply similar to a standard DM, and then we discuss those which are intertwined with a DM by a third, non invertible, operator, giving rise to what we call Riesz Density Matrix operator (RDM). After introducing the mathematical framework, we apply the framework to a couple of applications. The first application is related to a non-Hermitian Hamiltonian describing gain and loss phenomena, widely considered in the context of PT-quantum mechanics. The second application is related to a finite-dimensional version of the Swanson Hamiltonian, never considered before, and addresses the problem of deriving a milder version of the RDM when exceptional points form in the system.
Bagarello F., Gargano F., Saluto L. (2025). Density matrices and entropy operator for non-Hermitian quantum mechanics. JOURNAL OF MATHEMATICAL PHYSICS, 66(2) [10.1063/5.0231303].
Density matrices and entropy operator for non-Hermitian quantum mechanics
Bagarello F.;Gargano F.
;Saluto L.
2025-01-01
Abstract
In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyze two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy operator: we first consider those operators which are simply similar to a standard DM, and then we discuss those which are intertwined with a DM by a third, non invertible, operator, giving rise to what we call Riesz Density Matrix operator (RDM). After introducing the mathematical framework, we apply the framework to a couple of applications. The first application is related to a non-Hermitian Hamiltonian describing gain and loss phenomena, widely considered in the context of PT-quantum mechanics. The second application is related to a finite-dimensional version of the Swanson Hamiltonian, never considered before, and addresses the problem of deriving a milder version of the RDM when exceptional points form in the system.File | Dimensione | Formato | |
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