Bound states in curved quantum waveguides

Exner, Pavel; Šeba, P.

doi:10.1063/1.528538

Cited by 329 publications

(293 citation statements)

References 13 publications

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“…2͒. 17 The center curve in the bent and straight sections of ⍀, denoted C, is given by r ជ ϭ ជ (s)ϵ͓a(s),b(s)͔, where s is the arc length of C. Note the normalization ʈ ជ Ј(s)ʈϭ1, where prime denotes derivative with respect to s. The points in ⍀ are labeled in accordance with the parametrization…”

Section: Model and Equations Of Motionmentioning

confidence: 99%

Kink propagation and trapping in a two-dimensional curved Josephson junction

et al. 2004

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Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.

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Section: Model and Equations Of Motionmentioning

confidence: 99%

Kink propagation and trapping in a two-dimensional curved Josephson junction

et al. 2004

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“…As for the Dirichlet Laplacian −Δ Ωε D , it is well known [6,8,15,21] that the existence of discrete spectrum in unbounded strips is robust, i.e. independent of the sign of κ.…”

Section: Introductionmentioning

confidence: 99%

Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

Krejčiřı́k¹

2008

ESAIM: COCV

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Abstract.We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one is the biggest. We also show that the asymptotics can be obtained from a form of norm-resolvent convergence which takes into account the width-dependence of the domain of definition of the operators involved.Mathematics Subject Classification. 35P15, 49R50, 58J50, 81Q15.

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“…[1], [2], [3], [4], [5], [6] and references therein). Their spectral properties essentially depends on the geometry of the waveguide, especially the existence of bound states induced by curvature [1], [2], [3] or by coupling of straight waveguides through windows [4], [5] were shown. The waveguides with Neumann boundary condition were also investigated in several papers (e.g.…”

Section: Introductionmentioning

confidence: 99%

Bound states in straight quantum waveguides with combined boundary conditions

Dittrich

Křı́ž

2002

Journal of Mathematical Physics

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We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several statements on the existence or the absence of the discrete spectrum are proven for two models with combined boundary conditions. Examples of eigenfunctions and eigenvalues are computed numerically.

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Bound states in curved quantum waveguides

Cited by 329 publications

References 13 publications

Kink propagation and trapping in a two-dimensional curved Josephson junction

Kink propagation and trapping in a two-dimensional curved Josephson junction

Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

Bound states in straight quantum waveguides with combined boundary conditions

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