Density matrices and entropy operator for non-Hermitian quantum mechanics
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909462666674176 |
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| author | Bagarello, Fabio Gargano, Francesco Saluto, Lidia |
| author_facet | Bagarello, Fabio Gargano, Francesco Saluto, Lidia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density matrices and entropy operator for non-Hermitian quantum mechanics Bagarello, Fabio Gargano, Francesco Saluto, Lidia Mathematical Physics Quantum Physics 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. |
| title | Density matrices and entropy operator for non-Hermitian quantum mechanics |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2501.11537 |