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SIGMA, 2010, Volume 6, 098, 18 pages (Mi sigma556)  

This article is cited in 4 scientific papers (total in 4 papers)

Multi-Well Potentials in Quantum Mechanics and Stochastic Processes

Victor P. Berezovoj, Glib I. Ivashkevych, Mikhail I. Konchatnij

A. I. Akhiezer Institute of Theoretical Physics, National Scientific Center "Kharkov Institute of Physics and Technology", 1 Akademicheskaya Str., Kharkov, Ukraine

Abstract: 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.

Keywords: supersymmetry; solvability; partial breaking of $N=4$ supersymmetry; stochastic processes

DOI: https://doi.org/10.3842/SIGMA.2010.098

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/098/
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Bibliographic databases:

ArXiv: 1006.5917
MSC: 81Q60
Received: October 6, 2010; in final form December 1, 2010; Published online December 18, 2010
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Citation: Victor P. Berezovoj, Glib I. Ivashkevych, Mikhail I. Konchatnij, “Multi-Well Potentials in Quantum Mechanics and Stochastic Processes”, SIGMA, 6 (2010), 098, 18 pp.

Citation in format AMSBIB
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\paper Multi-Well Potentials in Quantum Mechanics and Stochastic Processes
\jour SIGMA
\yr 2010
\vol 6
\papernumber 098
\totalpages 18
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\crossref{https://doi.org/10.3842/SIGMA.2010.098}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fellows J.M., Smith R.A., “A new two-parameter family of potentials with a tunable ground state”, Journal of Physics A-Mathematical and Theoretical, 44:33 (2011), 335302  crossref  mathscinet  zmath  isi  scopus
    2. Berezovoj V.P., Konchatnij M.I., “Dynamics of Localized States in N=4 Susy Qm”, Phys. Part. Nuclei, 43:5 (2012), 654–658  crossref  adsnasa  isi  elib  scopus
    3. Berezovoj V.P., Konchatnij M.I., “Dynamics of Localized States in Extended Supersymmetric Quantum Mechanics with Multi-Well Potentials”, J. Phys. A-Math. Theor., 45:22 (2012), 225302  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Berezovoj V.P., Konchatnij M.I., Nurmagambetov A.J., “Tunneling Dynamics in Exactly Solvable Models with Triple-Well Potentials”, J. Phys. A-Math. Theor., 46:6 (2013), 065302  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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