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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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Інститут математики НАН України
2010
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146499 |
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irk-123456789-1464992019-02-10T01:25:44Z Multi-Well Potentials in Quantum Mechanics and Stochastic Processes Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146499 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. |
| spellingShingle |
Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. Multi-Well Potentials in Quantum Mechanics and Stochastic Processes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Berezovoj, V.P. Ivashkevych, G.I. Konchatnij, M.I. |
| author_sort |
Berezovoj, V.P. |
| title |
Multi-Well Potentials in Quantum Mechanics and Stochastic Processes |
| title_short |
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_sort |
multi-well potentials in quantum mechanics and stochastic processes |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146499 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT berezovojvp multiwellpotentialsinquantummechanicsandstochasticprocesses AT ivashkevychgi multiwellpotentialsinquantummechanicsandstochasticprocesses AT konchatnijmi multiwellpotentialsinquantummechanicsandstochasticprocesses |
| first_indexed |
2023-05-20T17:24:56Z |
| last_indexed |
2023-05-20T17:24:56Z |
| _version_ |
1796153245766254592 |