Density matrices and entropy operator for non-Hermitian quantum mechanics

被引:0
|
作者
Bagarello, F. [1 ,2 ]
Gargano, F. [1 ]
Saluto, L. [1 ]
机构
[1] Univ Palermo, Dipartimento Ingn, I-90128 Palermo, Italy
[2] INFN, Sez Catania, I-95123 Catania, Italy
关键词
ISOSPECTRAL POTENTIALS;
D O I
10.1063/5.0231303
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:14
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