Multi-Well Potentials in Quantum Mechanics and Stochastic Processes
Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146499 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes / V.P. Berezovoj, G.I. Ivashkevych, M.I. Konchatnij // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 43 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710603782553600 |
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| author | Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. |
| author_facet | Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. |
| citation_txt | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes / V.P. Berezovoj, G.I. Ivashkevych, M.I. Konchatnij // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 43 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions. The possibility of partial N=4 supersymmetry breaking is determined. We also obtain exact forms of multi-well potentials, both symmetric and asymmetric, using the Hamiltonian of harmonic oscillator as initial. The modification of the shape of potentials due to variation of parameters is also discussed, as well as application of the obtained results to the study of tunneling processes. We consider the case of exact, as well as partially broken N=4 supersymmetry. The distinctive feature of obtained probability densities and potentials is a parametric freedom, which allows to substantially modify their shape. We obtain the expressions for probability densities under the generalization of the Ornstein-Uhlenbeck process.
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| first_indexed | 2025-12-07T17:25:41Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146499 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:25:41Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
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| spelling | Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. 2019-02-09T19:17:40Z 2019-02-09T19:17:40Z 2010 Multi-Well Potentials in Quantum Mechanics and Stochastic Processes / V.P. Berezovoj, G.I. Ivashkevych, M.I. Konchatnij // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 43 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60 DOI:10.3842/SIGMA.2010.098 https://nasplib.isofts.kiev.ua/handle/123456789/146499 Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions. The possibility of partial N=4 supersymmetry breaking is determined. We also obtain exact forms of multi-well potentials, both symmetric and asymmetric, using the Hamiltonian of harmonic oscillator as initial. The modification of the shape of potentials due to variation of parameters is also discussed, as well as application of the obtained results to the study of tunneling processes. We consider the case of exact, as well as partially broken N=4 supersymmetry. The distinctive feature of obtained probability densities and potentials is a parametric freedom, which allows to substantially modify their shape. We obtain the expressions for probability densities under the generalization of the Ornstein-Uhlenbeck process. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 Authors thank to M. Plyushchay for helpful discussions and BVP Conference Organizers for a stimulating environment. We are thankful to A. Nurmagambetov for reading the manuscript, suggestions and improvings. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multi-Well Potentials in Quantum Mechanics and Stochastic Processes Article published earlier |
| spellingShingle | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. |
| title | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_full | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_fullStr | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_full_unstemmed | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_short | Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_sort | multi-well potentials in quantum mechanics and stochastic processes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146499 |
| work_keys_str_mv | AT berezovojvp multiwellpotentialsinquantummechanicsandstochasticprocesses AT ivashkevychgi multiwellpotentialsinquantummechanicsandstochasticprocesses AT konchatnijmi multiwellpotentialsinquantummechanicsandstochasticprocesses |