NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2012, 3 (5), P. 6–32
DIRECT AND INVERSE PROBLEMS IN THE MODEL OF QUANTUM GRAPHS
I.S. Lobanov – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, lobanov.igor@gmail.com.
E.S. Trifanova – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, etrifanova@gmail.com.
Here we present a detailed statement about solving of spectral and transport problems for quantum graphs. The practical prescriptions for finding the energy of pi-electrons and current-voltage characteristics for aromatic at the disposal of models of quantum graphs are suggested. We propose an algorithm increasing the precision of numerical solution and
discuss the facilities for parallel computations. Here we also suggest the method of inverse problem solution which plays an important role in engineering.
Keywords: quantum graphs, electronic properties, models of aromatic, algorithms of supercomputer modeling.
UDC 514.84, 530.145, 519.673, 538.915
PACS 72.80.Vp, 73.21.Hb, 73.22.Dj, 73.22.Pr, 73.63.Nm