Work

Density matrices and entropy operator for non-Hermitian quantum mechanics

Year: 2025

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0231303

Authors: F. Bagarello, F. Gargano, L. Saluto

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Catania, University of Palermo

Language: English

Topic: Quantum Mechanics and Non-Hermitian Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Università degli Studi di Palermo

Awards: G2060705543, G4708537983, G993508978