Time dependent quantum graph with loop
https://doi.org/10.17586/2220-8054-2017-8-4-420-425
Abstract
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.
Supporting agencies: 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
About the Authors
D. A. Eremin
Ogarev Mordovia State University
Russian Federation
Russian Federation
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
E. N. Grishanov
Ogarev Mordovia State University
Russian Federation
Russian Federation
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
O. G. Kostrov
Ogarev Mordovia State University
Russian Federation
Russian Federation
Department of Mathematics and IT
Bolshevistskaya Str. 68; Saransk
D. S. Nikiforov
ITMO University
Russian Federation
Russian Federation
Department of Higher Mathematics
197101; Kroverkskiy pr. 49; St. Petersburg
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Department of Higher Mathematics
197101; Kroverkskiy pr. 49; St. Petersburg
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Review
For citations:
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
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