Preview

Наносистемы: физика, химия, математика

Расширенный поиск

A model of an electron in a quantum graph interacting with a two-level system

https://doi.org/10.17586/2220-8054-2019-10-2-131-140

Аннотация

A model of an electron in a quantum graph interacting with a two-level system is considered. The operator describing the model has the form of sum of tensor products. Self-adjoint extensions and a scattering matrix are written in terms of a boundary triplet, corresponding to the considered symmetric operator. Diagrams of reflection are calculated and numerical results are discussed .

Об авторах

A. Boitsev
ITMO University
Россия


I. Popov
ITMO University
Россия


Список литературы

1. Dauber J., Oellers M., Venn F., Epping A., Watanabe K., Taniguchi T., Hassler F., Stampfer C. Aharonov-Bohm oscillations and magnetic focusing in ballistic graphene rings. Phys. Rev. B, 2017, 96, P. 205407.

2. Chakraborty T., Manaselyan A., Barseghyan M. Irregular Aharonov-Bohm effect for interacting electrons in a ZnO quantum ring. J Phys Condens Matter, 2017, 29(7), P. 075605.

3. Caudrelier V., Mintchev M., Ragoucy E. Exact scattering matrix of graphs in magnetic field and quantum noise. J. Math. Phys., 2014, 55, P. 083524.

4. Exner P., Lotoreichik V., Perez-Obiol A. On the bound states of magnetic Laplacians on wedges. Rep. Math. Phys, 2018, 82, P. 161–185.

5. Kurasov P., Serio A. Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions. Nanosystems: Phys. Chem. Math., 2015, 6(3), P. 309–319.

6. Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov-Bohm ring. Nanosystems: Phys. Chem. Math., 2018, 9(4), P. 457–463.

7. Chatterjee A., Smolkina M.O., Popov I.Y. Persistent current in a chain of two Holstein-Hubbard rings in the presence of Rashba spin-orbit interaction. Nanosystems: Phys. Chem. Math., 2019, 10(1), P. 50–62.

8. G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs. AMS, Providence, 2012.

9. Boitsev A.A., Brasche J., Malamud M., Neidhardt H., Popov I.Y. Boundary Triplets, Tensor Products and Point Contacts to Reservoirs Annales Henri Poincare, IET, 2018, 19(9), P. 2783–2837.

10. Derkach V. A., Malamud M. M., 1991, Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal., 95(1), P. 1–95.

11. Malamud M. M. Some classes of extensions of a Hermitian operator with lacunae, Ukra¨ın. Mat. Zh., 1992, 44(2), P. 215–233.

12. Malamud M. M., 1992, Some classes of extensions of a Hermitian operator with lacunae, Ukra¨ın. Mat. Zh., 44(2), P. 215–233.

13. Boitsev A. A., Brasche J., Neidhardt H., Popov I. Y., A model of electron transport through a boson cavity. Nanosystems: Phys. Chem. Math., 2018, 9, P. 171–178.

14. Behrndt J., Malamud M.M., Neidhardt H. Scattering matrices and Weyl functions. Proc. Lond. Math. Soc., 2008, 97, P. 568–598.

15. Kato T. Perturbation Theory for Linear Operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York 1966.

16. Yafaev D.R. Mathematical Scattering Theory: General Theory, Translations of Mathematical Monographs, 105. American Mathematical Society, Providence, RI, 1992.

17. Baumgartel H., Wollenberg M. Mathematical Scattering Theory, Akademie-Verlag, Berlin, 1983.

18. Donoghue W.F. Monotone Matrix Functions and Analytic Continuation, Springer Verlag, Berlin and New York, 1974.


Рецензия

Для цитирования:


 ,   . Наносистемы: физика, химия, математика. 2019;10(2):131-140. https://doi.org/10.17586/2220-8054-2019-10-2-131-140

For citation:


Boitsev A.A., Popov I.Y. A model of an electron in a quantum graph interacting with a two-level system. Nanosystems: Physics, Chemistry, Mathematics. 2019;10(2):131-140. https://doi.org/10.17586/2220-8054-2019-10-2-131-140

Просмотров: 56


Creative Commons License
Контент доступен под лицензией Creative Commons Attribution 4.0 License.


ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)