najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1138Research ArticleMATHEMATICSМАТЕМАТИКАVariational estimations of the eigenvalues for 3D quantum waveguides in a transverse electric fieldMatveevD. G.

Redmond, WA 

d.g.matveev@gmail.comPopovI. Yu.popov1955@gmail.comMicrosoftUnited StatesSaint Petersburg National Research University of Information Technologies, Mechanics and OpticsRussian Federation20121908202533622Copyright © Matveev D.G., Popov I.Y., 20252025Matveev D.G., Popov I.Y.Matveev D.G., 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/1138

It is shown that an eigenvalue of the Laplacian exists below the continuous spectrum for a system of threedimensional quantum waveguides laterally coupled via a small window and placed in a transverse electric field, and the estimation for the eigenvalue is obtained. A field induced shift of the eigenvalue is estimated by using a variation.

variational methodspectrum estimationsquantum waveguidesexternal fieldThe work was supported by Federal Targeted Program ”Scientific and Educational Human Resources for Innovation-Driven Russia” (contracts P689 NK-526P, 14.740.11.0879, and 16.740.11.0030), grant 11-08-00267 of Russian Foundation for Basic Researches and by Federal Targeted Program ”Researches and Development in the Priority Directions Developments of a Scientific and Technological Complex of Russia 2007-2013” (state contract 07.514.11.4146).ReferencesAlferov Zh. I., Aseev A. L., Gaponov S. V., Kop’ev P. S., Suris R. A. // In: Nanomaterials and Nanotechnologies, Part 1, Analytics. — Moscow, 2008 in Russian.Alferov Zh. I., Aseev A. L., Gaponov S. V., Kop’ev P. S., Suris R. A. // In: Nanomaterials and Nanotechnologies, Part 1, Analytics. — Moscow, 2008 in Russian.Ho J., Yerushalmi R., Jacobson Z. A., Fan Z., Alley R. L., Javey A. // Nature Mater. — 2008. — V. 7. — P. 62.Ho J., Yerushalmi R., Jacobson Z. A., Fan Z., Alley R. L., Javey A. // Nature Mater. — 2008. — V. 7. — P. 62.Ferry D.K., Goodnick S.M. Transport in Nanostructures. — Cambridge: Cambridge University Press, 1997.Ferry D.K., Goodnick S.M. Transport in Nanostructures. — Cambridge: Cambridge University Press, 1997.Zutic I., Fabian J., Das S. SARMA Spintronics: Fundamental and Applications // Rev. Mod. Phys. — 2004. — V. 76. — P. 323–386.Zutic I., Fabian J., Das S. SARMA Spintronics: Fundamental and Applications // Rev. Mod. Phys. — 2004. — V. 76. — P. 323–386.Bader S.D. Colloquium: Opportunities in nanomagnetism // Rev. Mod. Phys. — 2006. — V. 78. — P. 1–15.Bader S.D. Colloquium: Opportunities in nanomagnetism // Rev. Mod. Phys. — 2006. — V. 78. — P. 1–15.Grunberg P. Layered magnetic structures: facts, figures, future // J. Phys.: Condens. Matter. — 2001. — V. 13. — P. 7691–7706.Grunberg P. Layered magnetic structures: facts, figures, future // J. Phys.: Condens. Matter. — 2001. — V. 13. — P. 7691–7706.Exner P. Laterally coupled quantum waveguides // Cont. Math. — 1998. — V. 217. — P. 69–82.Exner P. Laterally coupled quantum waveguides // Cont. Math. — 1998. — V. 217. — P. 69–82.Matveev D. G., Popov I. Yu. Bound electron states in a system of coupled quantum waveguides in a transverse electric field // Tech. Phys. Lett. — 2009. — V. 35 (11). — P. 1007–1009.Matveev D. G., Popov I. Yu. Bound electron states in a system of coupled quantum waveguides in a transverse electric field // Tech. Phys. Lett. — 2009. — V. 35 (11). — P. 1007–1009.Exner P., Vugalter S. Bound state asymptotic estimates for window-coupled Dirichlet strips and layers // J. Phys. A: Math. Gen. — 1997. — V. 30. — P. 7863–7878.Exner P., Vugalter S. Bound state asymptotic estimates for window-coupled Dirichlet strips and layers // J. Phys. A: Math. Gen. — 1997. — V. 30. — P. 7863–7878.Melnichuk O.P., Popov I.Yu. Coupled dielectric waveguides: variational estimations // J. Math. Phys. — 2005. — V. 46, No. 7. — P. 073501/1-073591/17.Melnichuk O.P., Popov I.Yu. Coupled dielectric waveguides: variational estimations // J. Math. Phys. — 2005. — V. 46, No. 7. — P. 073501/1-073591/17.Popov I.Yu. Asymptotics of bound states and bands for laterally coupled waveguides and layers // J. Math. Phys. — 2002. — V. 43, No. 1. — P. 215–234.Popov I.Yu. Asymptotics of bound states and bands for laterally coupled waveguides and layers // J. Math. Phys. — 2002. — V. 43, No. 1. — P. 215–234.Popov I.Yu. Asymptotics of bound states and bands for laterally coupled three-dimensional waveguides // Rep. on Math. Phys. — 2001. — V. 48, No. 3.Popov I.Yu. Asymptotics of bound states and bands for laterally coupled three-dimensional waveguides // Rep. on Math. Phys. — 2001. — V. 48, No. 3.Bagraev N., Martin G., Pavlov B. S., Yafyasov A. Landau–Zener effect for a quasi-2D periodic sandvich // Nanosystems: Phys., Chem., Math. — 2011. — V. 2 (4). — P. 32-50.Bagraev N., Martin G., Pavlov B. S., Yafyasov A. Landau–Zener effect for a quasi-2D periodic sandvich // Nanosystems: Phys., Chem., Math. — 2011. — V. 2 (4). — P. 32-50.

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