najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-2-171-178najo-639Research ArticleMATHEMATICSМАТЕМАТИКАA model of electron transport through a boson cavityBoitsevA. A.

Kronverkskiy, 49, St. Petersburg, 197101

boitsevanton@gmail.comBrascheJ.

Erzstr. 1, D-38678 Clausthal-Zellerfeld

johannes.brasche@tu-clausthal.deNeidhardtH.

Mohrenstr. 39, D-10117 Berlin

hagen.neidhardt@wias-berlin.dePopovI. Y.

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comITMO UniversityRussian FederationInstitut fu¨r Mathematik, TU ClausthalGermanyWeierstrass InstituteGermany20181208202592171–178Copyright © Boitsev A.A., Brasche J., Neidhardt H., Popov I.Y., 20252025Boitsev A.A., Brasche J., Neidhardt H., Popov I.Y.Boitsev A.A., Brasche J., Neidhardt H., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/639

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 electro-magnetic 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.

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