Bound states in straight quantum waveguides with combined boundary conditions

Dittrich, J.; Křı́ž, Jan

doi:10.1063/1.1491597

Cited by 62 publications

(61 citation statements)

References 13 publications

(21 reference statements)

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“…vanishing of the normal derivative-cf. [DKř02b]. The idea of Theorem 3.4 and of its corollary comes from [DKř02a], where this result was proved under stronger assumptions.…”

Section: Notesmentioning

confidence: 99%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

143

133

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More information about this series at http://www.springer.com/series/720The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background material, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research.

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“…vanishing of the normal derivative-cf. [DKř02b]. The idea of Theorem 3.4 and of its corollary comes from [DKř02a], where this result was proved under stronger assumptions.…”

Section: Notesmentioning

confidence: 99%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

143

133

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“…In view of Theorem 3 this waveguide system has bound states. In particular, one expects that in the case when α 1 is close to zero and α 0 is large the spectral properties will be similar to those of the situation studied in [9]. Since the system is symmetric with respect to the y-axis, we can restrict ourselves to the part of Ω in the first quadrant and we may consider separately the symmetric and antisymmetric solutions, i.e.…”

Section: A 'Rectangular Well' Examplementioning

confidence: 99%

“…It can be done by imposing a combination of Dirichlet and Neumann boundary conditions on different parts of the boundary. Such models were studied in [9,10,17,20].…”

Section: Introductionmentioning

confidence: 99%

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Straight Quantum Waveguide with Robin Boundary Conditions

Jílek¹

2007

SIGMA

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Abstract. We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated eigenvalues and eigenfunctions are studied numerically by the mode-matching technique.

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“…The spectral results become richer if one considers a combination of Dirichlet and Neumann boundary conditions [16,17]. Here the problem is interesting even for straight strips and much less studied in the literature.…”

mentioning

confidence: 99%

On the Spectrum of Curved Planar Waveguides

Krejčiřı́k¹,

Křı́ž²

2005

Publ. Res. Inst. Math. Sci.

102

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The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is investigated. We prove that the essential spectrum as a set is stable under any curvature of the reference curve which vanishes at infinity and find various sufficient conditions which guarantee the existence of geometrically induced discrete spectrum. Furthermore, we derive a lower bound to the distance between the essential spectrum and the spectral threshold for locally curved strips. The paper is also intended as an overview of some new and old results on spectral properties of curved quantum waveguides.

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Bound states in straight quantum waveguides with combined boundary conditions

Cited by 62 publications

References 13 publications

Quantum Waveguides

Quantum Waveguides

Straight Quantum Waveguide with Robin Boundary Conditions

On the Spectrum of Curved Planar Waveguides

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