NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (4), P. 420–425
Time dependent quantum graph with loop
D. A. Eremin – Department of Mathematics and IT, Ogarev Mordovia State University, Bolshevistskaya Str. 68, Saransk, Russia
E. N. Grishanov – Department of Mathematics and IT, Ogarev Mordovia State University, Bolshevistskaya Str. 68, Saransk, Russia
O. G. Kostrov – Department of Mathematics and IT, Ogarev Mordovia State University, Bolshevistskaya Str. 68, Saransk, Russia
D. S. Nikiforov – Department of Higher Mathematics, ITMO University, Kroverkskiy pr. 49, St. Petersburg, 197101, Russia
I.Y. Popov – Department of Higher Mathematics, ITMO University, Kroverkskiy pr. 49, St. Petersburg, 197101, Russia; popov1955@gmail.com
A quantum graph, consisting of a ring and segment is considered. We deal with the free Schrödinger 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.
Keywords: quantum graph, spectrum, time evolution.
PACS 03.65.w, 02.30.Tb, 02.10.Db, 73.63.Nm
DOI 10.17586/2220-8054-2017-8-4-420-425