Planar waveguide with “twisted” boundary conditions: Small width

Борисов, Д. И.; Cardone, Giuseppe

doi:10.1063/1.3681895

Cited by 16 publications

(8 citation statements)

References 38 publications

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“…The main physical motivation comes in this case from acoustics; more general results on embedded eigenvalues in straight channels due to symmetric Neumann obstacles, not necessarily of zero measure, can be found in [DP98] or [KPV00]. The spectrum in the mixed-condition situation of Problem 4, which can be regarded as a twodimensional version of "twisted" boundary conditions, was found numerically in [DKř02b] using mode matching; the result suggests that the first critical value is a 1 ≈ 0.26 d, more recent results on such systems can be found in [BC11,BC12].…”

Section: Notesmentioning

confidence: 91%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

142

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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Section: Notesmentioning

confidence: 91%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

142

133

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“…On the other hand, a discrete spectrum may arise in a tube which is constantly twisted and the twist is locally slowed down [13]. Note that these results have a two-dimensional analogue, namely a Hardy inequality in planar strips where the Dirichlet and Neumann condition suddenly 'switch sides' [16] and the appearance of a nontrivial discrete spectrum when a sufficiently long purely Neumann segment is inserted in between [3,9].…”

Section: Introductionmentioning

confidence: 92%

Geometrically Induced Spectral Effects in Tubes with a Mixed Dirichlet—Neumann Boundary

Bakharev

Exner

2018

Reports on Mathematical Physics

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We investigate spectral properties of the Laplacian in L 2 (Q), where Q is a tubular region in R 3 of a fixed cross section, and the boundary conditions combined a Dirichlet and a Neumann part. We analyze two complementary situations, when the tube is bent but not twisted, and secondly, it is twisted but not bent. In the first case we derive sufficient conditions for the presence and absence of the discrete spectrum showing, roughly speaking, that they depend on the direction in which the tube is bent. In the second case we show that a constant twist raises the threshold of the essential spectrum and a local slowndown of it gives rise to isolated eigenvalues. Furthermore, we prove that the spectral threshold moves up also under a sufficiently gentle periodic twist.

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“…Two-dimensional straight waveguides with combined boundary conditions, classical as well as quantum, were considered in a number of papers [1]- [5]. Mostly the existence of isolated eigenvalues was studied.…”

Section: Introductionmentioning

confidence: 99%