Non-Hermitian oscillators with symmetry
We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing wi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Paolo Amore [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Annals of physics - Kidlington [u.a.] : Elsevier, 1957, 353(2015), Seite 238 |
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| Übergeordnetes Werk: |
volume:353 ; year:2015 ; pages:238 |
| Links: |
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| DOI / URN: |
10.1016/j.aop.2014.11.018 |
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OLC1965607071 |
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| 520 | |a We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. | ||
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| 650 | 4 | |a Non-Hermitian Hamiltonian | |
| 650 | 4 | |a Oscillators | |
| 700 | 0 | |a Francisco M. Fernández |4 oth | |
| 700 | 0 | |a Javier Garcia |4 oth | |
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10.1016/j.aop.2014.11.018 doi PQ20160617 (DE-627)OLC1965607071 (DE-599)GBVOLC1965607071 (PRQ)p510-1699368376441cbb9624989dddb1f085bc2ad13e9383bb077968196ae9a46d850 (KEY)0047092920150000353000000238nonhermitianoscillatorswithsymmetry DE-627 ger DE-627 rakwb eng 530 DNB 33.00 bkl Paolo Amore verfasserin aut Non-Hermitian oscillators with symmetry 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. PT-symmetry Point-group symmetry Physics Multidimensional systems Eigen values Space-time symmetry Non-Hermitian Hamiltonian Oscillators Francisco M. Fernández oth Javier Garcia oth Enthalten in Annals of physics Kidlington [u.a.] : Elsevier, 1957 353(2015), Seite 238 (DE-627)129514810 (DE-600)211006-4 (DE-576)014924218 0003-4916 nnns volume:353 year:2015 pages:238 http://dx.doi.org/10.1016/j.aop.2014.11.018 Volltext http://search.proquest.com/docview/1664189600 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_55 GBV_ILN_70 33.00 AVZ AR 353 2015 238 |
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10.1016/j.aop.2014.11.018 doi PQ20160617 (DE-627)OLC1965607071 (DE-599)GBVOLC1965607071 (PRQ)p510-1699368376441cbb9624989dddb1f085bc2ad13e9383bb077968196ae9a46d850 (KEY)0047092920150000353000000238nonhermitianoscillatorswithsymmetry DE-627 ger DE-627 rakwb eng 530 DNB 33.00 bkl Paolo Amore verfasserin aut Non-Hermitian oscillators with symmetry 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. PT-symmetry Point-group symmetry Physics Multidimensional systems Eigen values Space-time symmetry Non-Hermitian Hamiltonian Oscillators Francisco M. Fernández oth Javier Garcia oth Enthalten in Annals of physics Kidlington [u.a.] : Elsevier, 1957 353(2015), Seite 238 (DE-627)129514810 (DE-600)211006-4 (DE-576)014924218 0003-4916 nnns volume:353 year:2015 pages:238 http://dx.doi.org/10.1016/j.aop.2014.11.018 Volltext http://search.proquest.com/docview/1664189600 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_55 GBV_ILN_70 33.00 AVZ AR 353 2015 238 |
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10.1016/j.aop.2014.11.018 doi PQ20160617 (DE-627)OLC1965607071 (DE-599)GBVOLC1965607071 (PRQ)p510-1699368376441cbb9624989dddb1f085bc2ad13e9383bb077968196ae9a46d850 (KEY)0047092920150000353000000238nonhermitianoscillatorswithsymmetry DE-627 ger DE-627 rakwb eng 530 DNB 33.00 bkl Paolo Amore verfasserin aut Non-Hermitian oscillators with symmetry 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. PT-symmetry Point-group symmetry Physics Multidimensional systems Eigen values Space-time symmetry Non-Hermitian Hamiltonian Oscillators Francisco M. Fernández oth Javier Garcia oth Enthalten in Annals of physics Kidlington [u.a.] : Elsevier, 1957 353(2015), Seite 238 (DE-627)129514810 (DE-600)211006-4 (DE-576)014924218 0003-4916 nnns volume:353 year:2015 pages:238 http://dx.doi.org/10.1016/j.aop.2014.11.018 Volltext http://search.proquest.com/docview/1664189600 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_55 GBV_ILN_70 33.00 AVZ AR 353 2015 238 |
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10.1016/j.aop.2014.11.018 doi PQ20160617 (DE-627)OLC1965607071 (DE-599)GBVOLC1965607071 (PRQ)p510-1699368376441cbb9624989dddb1f085bc2ad13e9383bb077968196ae9a46d850 (KEY)0047092920150000353000000238nonhermitianoscillatorswithsymmetry DE-627 ger DE-627 rakwb eng 530 DNB 33.00 bkl Paolo Amore verfasserin aut Non-Hermitian oscillators with symmetry 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. PT-symmetry Point-group symmetry Physics Multidimensional systems Eigen values Space-time symmetry Non-Hermitian Hamiltonian Oscillators Francisco M. Fernández oth Javier Garcia oth Enthalten in Annals of physics Kidlington [u.a.] : Elsevier, 1957 353(2015), Seite 238 (DE-627)129514810 (DE-600)211006-4 (DE-576)014924218 0003-4916 nnns volume:353 year:2015 pages:238 http://dx.doi.org/10.1016/j.aop.2014.11.018 Volltext http://search.proquest.com/docview/1664189600 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_55 GBV_ILN_70 33.00 AVZ AR 353 2015 238 |
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We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. |
| abstractGer |
We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. |
| abstract_unstemmed |
We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of . Pairs of eigenvalues coalesce at exceptional points ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of . * PT-symmetric oscillators exhibit real eigenvalues. * Not all space-time symmetries lead to real eigenvalues. * Some Hamiltonians are invariant under unitary transformations. * Point-group symmetry greatly simplifies the calculation of eigenvalues and eigenfunctions. * Group theory and perturbation theory enable one to predict the occurrence of real eigenvalues. |
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| title_short |
Non-Hermitian oscillators with symmetry |
| url |
http://dx.doi.org/10.1016/j.aop.2014.11.018 http://search.proquest.com/docview/1664189600 |
| remote_bool |
false |
| author2 |
Francisco M. Fernández Javier Garcia |
| author2Str |
Francisco M. Fernández Javier Garcia |
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129514810 |
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| doi_str |
10.1016/j.aop.2014.11.018 |
| up_date |
2024-07-03T18:28:15.268Z |
| _version_ |
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