najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-4-457-463najo-701Research ArticleMATHEMATICSМАТЕМАТИКАWave dynamics on time-depending graph with Aharonov-Bohm ringEreminD. A.

Department of Mathematics and IT

Bolshevistskaya Str. 68, Saransk

ereminda@mail.ruGrishanovE. N.

Department of Mathematics and IT

Bolshevistskaya Str. 68, Saransk

evgenyg@mail.ruNikiforovD. S.

Department of Higher Mathematics

Kroverkskiy pr. 49, St. Petersburg, 197101

dmitrii.nikiforov@gmail.comPopovI. Y.

Department of Higher Mathematics

Kroverkskiy pr. 49, St. Petersburg, 197101

popov1955@gmail.comOgarev Mordovia State UniversityRussian FederationITMO UniversityRussian Federation20181308202594457463Copyright © Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y., 20252025Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y.Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/701

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.

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