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Hybrid form of quantum theory with non-Hermitian Hamiltonians
- 1.0570944 - ÚJF 2024 RIV NL eng J - Journal Article
Znojil, Miloslav
Hybrid form of quantum theory with non-Hermitian Hamiltonians.
Physics Letters. A. Roč. 457, JAN (2023), č. článku 128556. ISSN 0375-9601. E-ISSN 1873-2429
Institutional support: RVO:61389005
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)
Impact factor: 2.6, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.physleta.2022.128556
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.
Permanent Link: https://hdl.handle.net/11104/0342282
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