2025/01/20 by Fabio Bagarello, Bagarello, Fabio, Francesco Gargano +3 · 1 citation
Physics and Astronomy · Computer Science · #Quantum Mechanics and Non-Hermitian Physics #Quantum Information and Cryptography #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2501.11537
In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse 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 \em 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 waht 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.