Variational estimations of the eigenvalues for 3D quantum waveguides in a transverse electric field
Abstract
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.
Supporting agencies: The 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).
About the Authors
D. G. Matveev
Microsoft
United States
United States
Redmond, WA
I. Yu. Popov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Russian Federation
Russian Federation
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Review
For citations:
Matveev D.G., Popov I.Yu. Variational estimations of the eigenvalues for 3D quantum waveguides in a transverse electric field. Nanosystems: Physics, Chemistry, Mathematics. 2012;3(3):6-22.
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