Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

Abstract The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach an...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 55; no. 9; pp. 95202 - 95228
Main Authors Barrera-Figueroa, Víctor, Rabinovich, Vladimir S, Cristina Loredo-Ramírez, Samantha Ana
Format Journal Article
LanguageEnglish
Published IOP Publishing 04.03.2022
Subjects
adiabatic approach
Green function
slowly varying tube
spectral parameter power series (SPPS) method
tunnel effect
wave function
Wentzel–Kramers–Brillouin (WKB) approximation
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Summary:Abstract The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach and the WKB approximation. Unlike other similar studies, in the present work we consider arbitrary bounded potentials and obtain exact solutions for the thresholds, and for the transverse modes in the form of power series of the spectral parameter. Our approach leads to an effective numerical method for the analysis of such quantum waveguides and for the tunnel effect observed in sections of the waveguide that shrink or widen too much. Several examples of interest show the applicability of the method.
Bibliography:JPhysA-116760.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac4b14