Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics
Non-Hermitian quantum-Hamiltonian-candidate combination <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>λ</mi> </msub> </semantics> </math> </inline-formula> of a non-Hermitian unper...
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MDPI AG
2020-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/1/80 |
| _version_ | 1798024329794945024 |
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| author | Miloslav Znojil |
| author_facet | Miloslav Znojil |
| author_sort | Miloslav Znojil |
| collection | DOAJ |
| description | Non-Hermitian quantum-Hamiltonian-candidate combination <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>λ</mi> </msub> </semantics> </math> </inline-formula> of a non-Hermitian unperturbed operator <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <mo>=</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> with an arbitrary “small” non-Hermitian perturbation <inline-formula> <math display="inline"> <semantics> <mrow> <mi>λ</mi> <mi>W</mi> </mrow> </semantics> </math> </inline-formula> is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh−Schrödinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed. |
| first_indexed | 2024-04-11T18:00:26Z |
| format | Article |
| id | doaj.art-0308fb2b935d4d3082d38efa78a473ea |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T18:00:26Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-0308fb2b935d4d3082d38efa78a473ea2022-12-22T04:10:30ZengMDPI AGEntropy1099-43002020-01-012218010.3390/e22010080e22010080Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum MechanicsMiloslav Znojil0Institute of System Science, Durban University of Technology, P. O. Box 1334, Durban 4000, South AfricaNon-Hermitian quantum-Hamiltonian-candidate combination <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>λ</mi> </msub> </semantics> </math> </inline-formula> of a non-Hermitian unperturbed operator <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <mo>=</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> with an arbitrary “small” non-Hermitian perturbation <inline-formula> <math display="inline"> <semantics> <mrow> <mi>λ</mi> <mi>W</mi> </mrow> </semantics> </math> </inline-formula> is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh−Schrödinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed.https://www.mdpi.com/1099-4300/22/1/80hidden hermiticityhilbert space metricsize of perturbationsstabilitypt symmetryunitary quantum evolution |
| spellingShingle | Miloslav Znojil Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics Entropy hidden hermiticity hilbert space metric size of perturbations stability pt symmetry unitary quantum evolution |
| title | Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics |
| title_full | Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics |
| title_fullStr | Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics |
| title_full_unstemmed | Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics |
| title_short | Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics |
| title_sort | theory of response to perturbations in non hermitian systems using five hilbert space reformulation of unitary quantum mechanics |
| topic | hidden hermiticity hilbert space metric size of perturbations stability pt symmetry unitary quantum evolution |
| url | https://www.mdpi.com/1099-4300/22/1/80 |
| work_keys_str_mv | AT miloslavznojil theoryofresponsetoperturbationsinnonhermitiansystemsusingfivehilbertspacereformulationofunitaryquantummechanics |