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Hybrid form of quantum theory with non-Hermitian Hamiltonians
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SYSNO ASEP 0570944 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Hybrid form of quantum theory with non-Hermitian Hamiltonians Author(s) Znojil, Miloslav (UJF-V) RID, ORCID, SAI Number of authors 1 Article number 128556 Source Title Physics Letters. A. - : Elsevier - ISSN 0375-9601
Roč. 457, JAN (2023)Number of pages 5 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords Non -Hermitian quantum mechanics of unitary systems ; Hiddenly Hermitian quantum Hamiltonians ; Factorized Dyson map ; Hermitization using a combined ; amendment of the inner product and ; Hamiltonian OECD category Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Method of publishing Limited access Institutional support UJF-V - RVO:61389005 UT WOS 000957963800002 EID SCOPUS 85142372103 DOI 10.1016/j.physleta.2022.128556 Annotation In Schrodinger picture the unitarity of evolution is usually guaranteed by the Hermiticity of the Hamiltonian operator 1) = 1)dagger in a conventional Hilbert space Htextbook. After a Dyson-inspired operatortransformation (OT) non-unitary preconditioning S2 : 1) -> H the simplified Hamiltonian H is, in its manifestly unphysical Hilbert space Hauxiliary, non-Hermitian. Besides its natural OT-based physical interpretation it can also be 'Hermitized' (i.e., made compatible with the unitarity) via a metric-amendment (MA) change of the Hilbert space, Hauxiliary -> Hphysical. In our present letter we propose another, third, hybrid form (HF) of the Hermitization of H in which the change involves, simultaneously, both the Hamiltonian and the metric. Formally this means that the original Dyson map is assumed factorizable, S2 = S2MS2H. A key practical advantage of the new HF approach lies in the model-dependent adaptability of such a factorization. The flexibility and possible optimality of the balance between the MA-related (i.e., metric-amending) factor S2M and the OT-related (i.e., Hamiltonian-changing) factor S2H are explicitly illustrated via an elementary two-state quantum model. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2024 Electronic address https://doi.org/10.1016/j.physleta.2022.128556
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