Wave dynamics on time-depending graph with Aharonov-Bohm ring
https://doi.org/10.17586/2220-8054-2018-9-4-457-463
Аннотация
Aharonov–Bohm ring (AB ring) is an element frequently used in nanosystems. The paper deals with wave dynamics on quantum graph consisting of AB ring coupled to a segment. It is assumed that the lengths of the edges vary in time. Variable replacement is made to come to the problem for stationary geometric graph. The obtained equation is solved using the expansion with respect to a complete system of eigenfunctions of the unperturbed self-adjoint operator for the stationary graph. The coefficients of the expansion are found as solutions of a system of differential equations numerically. The influence of the magnetic field is studied. The comparison with the case of stable geometric graph is made.
Об авторах
D. Eremin
Ogarev Mordovia State University
Россия
Россия
E. Grishanov
Ogarev Mordovia State University
Россия
Россия
D. Nikiforov
ITMO University
Россия
Россия
I. Popov
ITMO University
Россия
Россия
Список литературы
1. Aharonov Y., Bohm D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev., 1959, 115, P. 485–491.
2. Lena C. Eigenvalues variations for Aharonov-Bohm operators. ´ J. Math. Phys, 2015, 56, P. 011502.
3. Fischer A.M., CampoV.L., Jr., Portnoi M.E., Romer R.A. Exciton Storage in a Nanoscale AharonovBohm Ring with Electric Field Tuning. Phys. Rev. Lett., 2009, 102, P. 096405.
4. Entin-Wohlman O., Imry Y., Aharony A. Effects of external radiation on biased Aharonov-Bohm rings. Phys. Rev. B, 2004, 70, P. 075301.
5. Shelykh I. A., Galkin N. G., Bagraev N. T. Conductance of a gated AharonovBohm ring touching a quantum wire, Phys. Rev. B, 2006, 74, P. 165331.
6. Nichele F., Komijani Y., Hennel S., Ger C., Wegscheider W., Reuter D., Wieck A. D., Ihn T., Ensslin K. AharonovBohm rings with strong spinorbit interaction: the role of sample-specific properties. New J. Phys., 2013, 15, P. 033029
7. Kurasov P., Enerback. Aharonov-Bohm ring touching a quantum wire: ow to model it and to solve the inverse problem. ¨ Rep. Math. Phys., 2011, 68, P. 271–287.
8. Kokoreva M. A., Margulis V. A., Pyataev M. A. Electron transport in a two-terminal AharonovBohm ring with impurities. Physica E, 2011, 43, P. 1610–1634.
9. Kokoreva M. A., Pyataev M. A. Spectral and transport properties of one-dimensional nanoring superlattice.. Int. J. Mod. Phys. B, 2013, 27(20), P. 1350103.
10. Grishanov E.N., Eremin D.A., Ivanov D.A., Popov I.Y., Smirnov P.I. Periodic chain of disks in a magnetic field: bulk states and edge states. Nanosystems: Physics, Chemistry, Mathematics., 2015, 6(5), P. 637–643.
11. N. I. Gerasimenko, B. S. Pavlov, Scattering problems on noncompact graphs. Theoret. Math. Phys., 1988, 74, P. 230–240.
12. P. Exner, P. Keating, P. Kuchment, T. Sumada, A. Teplyaev,Analysis on graph and its applications. Proc. Symp. Pure Math. Providence, RI, 2008, 77.
13. P. Duclos, P. Exner, O. Turek. On the spectrum of a bent chain graph. J. Phys. A: Math. Theor., 2008, 41, P. 415206/1-18.
14. I.Y.Popov, A.N.Skorynina, I.V.Blinova. On the existence of point spectrum for branching strips quantum graph. J. Math. Phys., 2014, 55, P. 033504/1-20.
15. I. Y. Popov, P. I. Smirnov, Spectral problem for branching chain quantum graph. Phys. Lett., 2013, A 377, P. 439–442.
16. J.V. Jose, R. Gordery. Study of a quantum Fermi-acceleration model. Phys. Rev. Lett., 1986, 56, P. 290.
17. A.J. Makowski, S.T. Dembinski. Exactly solvable models with time-dependent boundary conditions. Phys. Lett., 1991, A,154(5-6), P. 217– 220.
18. C. Cacciapuoti, A. Mantile, A. Posilicano. Time dependent delta-prime interactions in dimension one. Nanosystems: Phys. Chem. Math., 2016, 7(2), P. 303–314.
19. Z.A. Sobirov, D.U. Matrasulov, Sh. Ataev and H. Yusupov In Complex Phenomena in Nanoscale Systems. Eds. G. Casati, D. Matrasulov. Berlin, Springer, 2009.
20. D.U. Matrasulov, J.R. Yusupov, K.K. Sabirov, Z.A. Sobirov. Time-dependent quantum graph. Nanosystems: Phys. Chem. Math., 2015, 6(2), P. 173–181.
21. O. Karpova, K. Sabirov, D. Otajanov, A. Ruzmetov, A.A. Saidov. Absorbing boundary conditions for Schrodinger equation in a time- ¨ dependent interval. Nanosystems: Phys. Chem. Math., 2017, 8(1), P. 13–19.
22. Eremin D.A., Grishanov E.N., Kostrov O.G., Nikiforov D.S., Popov I.Y. Time dependent quantum graph with loop. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8, P. 420–425.
23. Popov I.Y., Nikiforov D.S. Classical and quantum wave dynamics on time-dependent geometric graph. Chinese Journal of Physics. 2018, 56(2), P. 747–753.
24. Marquardt F., Bruder C. Aharonov-Bohm ring with fluctuating flux. Phys. Rev. B, 2002, 65, P. 125315.
Рецензия
Для цитирования:
, , , . Наносистемы: физика, химия, математика. 2018;9(4):457-463. https://doi.org/10.17586/2220-8054-2018-9-4-457-463
For citation:
Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov-Bohm ring. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(4):457-463. https://doi.org/10.17586/2220-8054-2018-9-4-457-463
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