Time dependent quantum graph with loop
https://doi.org/10.17586/2220-8054-2017-8-4-420-425
Аннотация
A quantum graph, consisting of a ring and segment is considered. We deal with the free Schr¨odinger ooperator at the edges and Kirchhoff conditions at the internal vertex. The lengths of the graph edges varies in time. Time evolution of wave packet is studied for different parameters of length varying law.
При поддержке: This work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by grant MK-5161.2016.1 of the President of the Russian Federation, DFG Grant NE 1439/3-1, by grant 16-11-10330 of Russian Science Foundation
Об авторах
D. A. Eremin
Ogarev Mordovia State University
Россия
Россия
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
E. N. Grishanov
Ogarev Mordovia State University
Россия
Россия
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
O. G. Kostrov
Ogarev Mordovia State University
Россия
Россия
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
D. S. Nikiforov
ITMO University
Россия
Россия
Department of Higher Mathematics
197101; Kroverkskiy pr. 49; St. Petersburg
I. Y. Popov
ITMO University
Россия
Россия
Department of Higher Mathematics
197101; Kroverkskiy pr. 49; St. Petersburg
Список литературы
1. Pauling L. The Diamagnetic Anisotropy of Aromatic Molecules. J. Chem. Phys., 1936, 4, P. 673.
2. Gerasimenko N.I., Pavlov B.S. Scattering problems on noncompact graphs. Theoret. Math. Phys., 1988, 74, P. 230–240.
3. Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H. with an appendix by P. Exner. Solvable Models in Quantum Mechanics: Second Edition, 2005. (Providence, R.I.: AMS Chelsea Publishing).
4. Pavlov B.S. The theory of extensions and explicity-solvable models. Russ. Math. Surv., 1987, 42(6), P. 127–168.
5. Popov I.Y., Kurasov P.A., Naboko S.N., Kiselev A.A., Ryzhkov A.E., Yafyasov A.M., Miroshnichenko G.P., Karpeshina Yu.E., Kruglov V.I., Pankratova T.F., Popov A.I. A distinguished mathematical physicist Boris S. Pavlov. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7, P. 782–788.
6. Exner P., Keating P., Kuchment P., Sumada T., Teplyaev A. Analysis on graph and its applications. Proc. Symp. Pure Math. Providence, RI, 2008, 77.
7. Duclos P., Exner P., Turek O. On the spectrum of a bent chain graph. J. Phys. A: Math. Theor., 2008, 41, P. 415206/1-18.
8. Popov I.Y., Skorynina A.N., Blinova I.V. On the existence of point spectrum for branching strips quantum graph. J. Math. Phys., 2014, 55, P. 033504/1-20.
9. Popov I.Y., Smirnov P.I. Spectral problem for branching hain quantum graph. Phys. Lett., 2013, A 377, P. 439–442.
10. Jose J.V., Gordery R. Study of a quantum Fermi-acceleration model. Phys. Rev. Lett., 1986, 56, P. 290.
11. Makowski A.J., Dembinski S.T. Exactly solvable models with ime-dependent boundary conditions. Phys. Lett., 1991, A, 154(5-6), P. 217–220.
12. Cacciapuoti C., Mantile A., Posilicano A. Time dependent delta-prime interactions in dimension one. Nanosystems: Phys. Chem. Math., 2016, 7(2), P. 303–314.
13. Matrasulov D.U., Yusupov J.R., Sabirov K.K., Sobirov Z.A. Time-dependent quantum graph. Nanosystems: Phys. Chem. Math., 2015, 6(2), P. 173–181.
14. Karpova O., Sabirov K., Otajanov D., Ruzmetov A., Saidov A.A. Absorbing boundary conditions for Schr¨odinger equation in a time-dependent interval. Nanosystems: Phys. Chem. Math., 2017, 8(1), P. 13–19.
Рецензия
Для цитирования:
Eremin D.A., Grishanov E.N., Kostrov O.G., Nikiforov D.S., Popov I.Y. Time dependent quantum graph with loop. Наносистемы: физика, химия, математика. 2017;8(4):420-425. https://doi.org/10.17586/2220-8054-2017-8-4-420-425
For citation:
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(4):420-425. https://doi.org/10.17586/2220-8054-2017-8-4-420-425
Просмотров:
47
Послать статью по эл. почте 