Scattering on a chain of zero-range potentials with internal structure in the stochastic magnetic field
https://doi.org/10.17586/2220-8054-2018-9-6-703-710
Abstract
Scattering problem on an infinite chain of zero-range potentials with internal structure in the stochastic magnetic field is investigated. Model operator is constructed using the perturbation theory for the self-adjoint operators. The relations with the scattering problem without stochasticity are investigated.
Supporting agencies: This work was initiated by my professor B.S. Pavlov, an outstanding mathematician of the St. Petersburg mathematical school who passed away more than two years ago.
About the Author
A. E. Ryzhkov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, St. Petersburg, 197101
References
1. Berezin F.A., Faddeev L.D. Remark on the Schrodinger equation with singular potential.¨ Dokl. Akad. Nauk SSSR, 1961, 137(5), P. 1011– 1014 (in Russian).
2. Pavlov B.S. Model of a zero-range potential with internal structure. Theoret. and Math. Phys., 1984, 59(3), P. 544–550.
3. Pavlov B.S., The theory of extensions and explicitly-soluble models. Russian Math. Surveys, 1987, 42(6), P. 127–168.
4. Albeverio S. and Kurasov P. Singular perturbations of differential operators. Solvable Schrodinger type operators. London Mathematical Society Lecture Notes 271, Cambridge Univ. Press, Cambridge 2000, 444 p.
5. Boitsev A.A., Neidhardt H., Popov I.Y. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7(2), P. 332–339.
6. Pavlov B.S., Ryzhkov A.E. Scattering on a random point potential, in P.Exner, P.Seba Applications of Self-Adjoint Extensions in Quantum Physics, Lecture Notes in Physics no 324, Springer-Verlag, Berlin-Heidelberg-New York, 1989, P. 100–114.
7. Ryzhkov A.E. Scattering of the acoustic waves on a Markovian point defect, in P. Exner, P. Seba. Schroedinger Operators, Standard and Nonstandard, World Scientific, Singapore, 1989, P. 407–409.
8. Albeverio S., Gesztesy F., Hoegh-Krohn R. and Holden H., with an appendix by P. Exner. Solvable Models in Quantum Mechanics, 2-nd ed., American Mathematical Society, Providence, Rhode Island, 2005, 488 p.
9. Karpeshina Yu.E. Eigenfunction-expansion theorem of scattering problems on one-dimensional periodic supports of the chain type in three-dimensional space. Problemy Mat. Fiz., 1983, 10, P. 137–163 (in Russian).
10. Subramanian R. Some applications of the method of zero-range potentials in quantum mechanics. Author’s Abstract of Candidate’s Dissertation, Leningrad State University, 1986 (in Russian).
11. Kurasov P.B., Pavlov B.S. Electron in a homogeneous crystal of point atoms with internal structure. II. Theoret. and Math. Phys., 1988, 74(1), P. 58–66.
Review
For citations:
Ryzhkov A.E. Scattering on a chain of zero-range potentials with internal structure in the stochastic magnetic field. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(6):703–710. https://doi.org/10.17586/2220-8054-2018-9-6-703-710
Views:
4
Email this article 