najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-5-611-617najo-974Research ArticleMATHEMATICSМАТЕМАТИКАWaveguide bands for a system of macromoleculesAdamyanV. M.

Dvoryanskaya str., 2, Odessa, 65082

BlinovaI. V.

Kronverkskiy, 49, Saint Petersburg, 197101

PopovA. I.

Kronverkskiy, 49, Saint Petersburg, 197101

PopovI. Yu.

Kronverkskiy, 49, Saint Petersburg, 197101

popov1955@gmail.comOdessa I. I. Mechnikov National UniversityUkraineITMO UniversityRussian Federation20151508202565611617Copyright © Adamyan V.M., Blinova I.V., Popov A.I., Popov I.Y., 20252025Adamyan V.M., Blinova I.V., Popov A.I., Popov I.Y.Adamyan V.M., Blinova I.V., Popov A.I., 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/974

A system of parallel chain-type macromolecules (linear polymers) is considered. The spectrum of an electron in such a system is described. Waveguide bands are shown to be present, ensuring conductivity. Consideration is undertaken within the framework of a zero-range potentials model based on the theory of self-adjoint extensions of symmetric operators. Possible applications also discussed. 

spectrumlinear polymerzero-range potentialThis work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Projects No 14.Z50.31.0031 and No. 1.754.2014/K), by grant MK-5001.2015.1 of the President of the Russian Federation, and by grant of St. Petersburg.ReferencesI.Yu. Popov. On the possibility of magnetoresistance governed by light. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 795–799.I.Yu. Popov. On the possibility of magnetoresistance governed by light. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 795–799.U. Wulf, M. Krahlisch, J. Kucera, H. Richter, J. Hontschel. A quantitative model for quantum transport in nano-transistors. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 800–809.U. Wulf, M. Krahlisch, J. Kucera, H. Richter, J. Hontschel. A quantitative model for quantum transport in nano-transistors. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 800–809.I. S. Lobanov, A. I. Trifanov, E. S. Trifanova. Genetic algorithm for constructing graphene nanoribbon with given electronic transport properties. Nanosystems: Phys. Chem. Math., 2013, 4(4), P. 512–523.I. S. Lobanov, A. I. Trifanov, E. S. Trifanova. Genetic algorithm for constructing graphene nanoribbon with given electronic transport properties. Nanosystems: Phys. Chem. Math., 2013, 4(4), P. 512–523.I.Yu.Popov, A.N.Skorynina, I.V.Blinova. On the existence of point spectrum for branching strips quantum graph. J. Math. Phys., 2014, 55, 033504/1-20.I.Yu.Popov, A.N.Skorynina, I.V.Blinova. On the existence of point spectrum for branching strips quantum graph. J. Math. Phys., 2014, 55, 033504/1-20.A.A.Boitsev, I.Yu.Popov, O.V.Sokolov. Hamiltonian with zero-range potentials having infinite number of eigenvalues. Nanosystems: Phys. Chem. Math., 2012, 3(4), P. 9–19.A.A.Boitsev, I.Yu.Popov, O.V.Sokolov. Hamiltonian with zero-range potentials having infinite number of eigenvalues. Nanosystems: Phys. Chem. Math., 2012, 3(4), P. 9–19.S.Albeverio, F.Gesztesy, R.Hoegh-Krohn, H.Holden with an appendix by P.Exner 2005 Solvable Models in Quantum Mechanics: Second Edition. (Providence, R.I.: AMS Chelsea Publishing)S.Albeverio, F.Gesztesy, R.Hoegh-Krohn, H.Holden with an appendix by P.Exner 2005 Solvable Models in Quantum Mechanics: Second Edition. (Providence, R.I.: AMS Chelsea Publishing)B.S.Pavlov, Extensions theory and explicitly solvable models. Uspekhi. Mat. Nauk., 1987, 42(6), P. 99– 131.B.S.Pavlov, Extensions theory and explicitly solvable models. Uspekhi. Mat. Nauk., 1987, 42(6), P. 99– 131.J.Berndt , M. M. Malamud, H. Neidhardt. Scattering matrices and Weyl functions. Proc. London Math. Soc., 2008, 97(3), P. 568–598.J.Berndt , M. M. Malamud, H. Neidhardt. Scattering matrices and Weyl functions. Proc. London Math. Soc., 2008, 97(3), P. 568–598.A.A. Boitsev, H. Neidhardt, I.Yu. Popov. Weyl function for sum of operators tensor products. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 747–759.A.A. Boitsev, H. Neidhardt, I.Yu. Popov. Weyl function for sum of operators tensor products. Nanosystems: Phys. Chem. Math., 2013, 4(6), P. 747–759.M. S. Birman, M. Z. Solomyak. Spectral Theory of Self-Adjoint Operators in Hilbert Space (D. Reidel Publishing Company, Dordrecht-Boston-Lancaster, 1987).M. S. Birman, M. Z. Solomyak. Spectral Theory of Self-Adjoint Operators in Hilbert Space (D. Reidel Publishing Company, Dordrecht-Boston-Lancaster, 1987).A. Alonso, B. Simon. The Birman-Krein-Vishik theory of selfadjoint extensions of semi-bounded operators. J. Oper. Theory, 1980, 4, P. 251–270.A. Alonso, B. Simon. The Birman-Krein-Vishik theory of selfadjoint extensions of semi-bounded operators. J. Oper. Theory, 1980, 4, P. 251–270.V.M. Adamyan, B.S. Pavlov. Null-range potentials and M.G. Krein’s formula for generalized resolvents. Journal of Soviet Mathematics, 1988, 42(2), P. 1537–1550.V.M. Adamyan, B.S. Pavlov. Null-range potentials and M.G. Krein’s formula for generalized resolvents. Journal of Soviet Mathematics, 1988, 42(2), P. 1537–1550.

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