najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-6-703-710najo-719Research ArticleMATHEMATICSМАТЕМАТИКАScattering on a chain of zero-range potentials with internal structure in the stochastic magnetic fieldRyzhkovA. E.

Kronverkskiy, 49, St. Petersburg, 197101

verdad60@mail.ruITMO UniversityRussian Federation20181408202596703–710Copyright © Ryzhkov A.E., 20252025Ryzhkov A.E.Ryzhkov A.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/719

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.

operator extensionstochastic magnetic fieldscattering problemThis 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.ReferencesBerezin 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).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).Pavlov B.S. Model of a zero-range potential with internal structure. Theoret. and Math. Phys., 1984, 59(3), P. 544–550.Pavlov B.S. Model of a zero-range potential with internal structure. Theoret. and Math. Phys., 1984, 59(3), P. 544–550.Pavlov B.S., The theory of extensions and explicitly-soluble models. Russian Math. Surveys, 1987, 42(6), P. 127–168.Pavlov B.S., The theory of extensions and explicitly-soluble models. Russian Math. Surveys, 1987, 42(6), P. 127–168.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.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.Boitsev A.A., Neidhardt H., Popov I.Y. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7(2), P. 332–339.Boitsev A.A., Neidhardt H., Popov I.Y. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7(2), P. 332–339.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.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.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.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.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.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.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).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).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).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).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.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.

The authors declare that there are no conflicts of interest present.