NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2018, 9 (2), P. 171–178
A model of electron transport through a boson cavity
A. A. Boitsev – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia; firstname.lastname@example.org
J. Brasche – Institut für Mathematik, TU Clausthal, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany; email@example.com
H. Neidhardt – Weierstrass Institute, Mohrenstr. 39, D-10117 Berlin, Germany; firstname.lastname@example.org
I.Y. Popov – ITMO University, Kronverkskiy, 49, St. Petersburg, 197101, Russia; email@example.com
We propose a model describing electronic transport through a boson cavity. We use the Jaynes–Cummings model dealing with a two-level quantum dot coupled to a quantized electromagnetic field and two semi-infinite wires. The mathematical background of our model is given by the theory of self-adjoint extensions of symmetric operators. Using the boundary triplets approach, the gamma-field and the Weyl function were calculated. In addition, we obtained the scattering matrix for the model system.
Keywords: boundary triplets, extensions, scattering, solvable model.
PACS 85.60.Jb, 88.40.H, 85.35.Be, 73.63.Kv, 42.50.Pq