Bound states and threshold resonances in quantum wires with circular bends

Kang, Lin; Rl, Jaffe

doi:10.1103/physrevb.54.5750

Cited by 27 publications

(30 citation statements)

References 13 publications

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“…Comparing this figure with Fig. 4 in [22] or Fig. 5 in [24], where the authors study the planar waveguide comprised of two straight regions connected by a region of constant curvature (with Dirichlet or mixed boundary conditions, respectively), we may see the similar behavior of the eigenvalues below the fundamental propagation constant.…”

Section: Numerical Resultsmentioning

confidence: 94%

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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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Section: Numerical Resultsmentioning

confidence: 94%

“…It is known, that a deviation from the straight tube can give rise to non-trivial spectral properties like existence of bound states, by bending it [6,11,15,18,21,22,24], introducing an arbitrarily small 'bump' [3,5] or impurities modeled by Dirac interaction [14], coupling several waveguides by a window [16], etc.…”

Section: Introductionmentioning

confidence: 99%

Straight Quantum Waveguide with Robin Boundary Conditions

Jílek¹

2007

SIGMA

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“…Importantly, a tight bend means that significant mode excitation can occur at very low energies. Larger bends generally require larger propagation energies to obtain the same degree of excitation, but the interface matching method encounters convergence difficulties at higher energies due to the coupling to strongly closed modes [16,26]. In the time-dependent calculations, we use cigar shaped wave packets with average energies of 2.225 and 3.57 for comparison.…”

Section: Circular Bend Calculationsmentioning

confidence: 99%

Manifestations of vortices during ultracold-atom propagation through waveguides

Bromley

Esry

2004

Phys. Rev. A

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The possibility of generating vortices during matter-wave propagation through microstructures is examined. Vortices can arise solely due to wave interference in low-density ultracold atom clouds, and do not require any atom-atom (nonlinear) interactions. The properties of these "interference vortices" are understood from a simple two-mode model in a straight waveguide. This model is then applied to vortex creation in a circular bend since a circular waveguide bend is one of the simplest atom optical elements that can induce mode excitations. Time-independent and time-dependent analyses are used to investigate vortex creation and dynamics in these systems.

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“…The research has given valuable knowledge on the physical behaviour but also reports on the limitations of the methods used. For instance, Lin & Jaffe [2] report that a straightforward matching at the boundary of a circular bend does not converge, demonstrating the numerical problems with such a method. An illposedness is present in quantum tube scattering and some type of regularisation is therefore required to avoid large errors.…”

Section: Introductionmentioning

confidence: 99%

Scattering in Quantum Tubes

Nilsson

2001

Foundations of Probability and Physics

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It is possible to fabricate mesoscopic structures where at least one of the dimensions is of the order of de Broglie wavelength for cold electrons. By using semiconductors, composed of more than one material combined with a metal slip-gate, two-dimensional quantum tubes may be built. We present a method for predicting the transmission of lowtemperature electrons in such a tube. This problem is mathematically related to the transmission of acoustic or electromagnetic waves in a twodimensional duct. The tube is asymptotically straight with a constant cross-section. Propagation properties for complicated tubes can be synthesised from corresponding results for more simple tubes by the so-called Building Block Method. Conformal mapping techniques are then applied to transform the simple tube with curvature and varying cross-section to a straight, constant cross-section, tube with variable refractive index. Stable formulations for the scattering operators in terms of ordinary differential equations are formulated by wave splitting using an invariant imbedding technique. The mathematical framework is also generalised to handle tubes with edges, which are of large technical interest. The numerical method consists of using a standard MATLAB ordinary differential equation solver for the truncated reflection and transmission matrices in a Fourier sine basis. It is proved that the numerical scheme converges with increasing truncation.

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Bound states and threshold resonances in quantum wires with circular bends

Cited by 27 publications

References 13 publications

Straight Quantum Waveguide with Robin Boundary Conditions

Straight Quantum Waveguide with Robin Boundary Conditions

Manifestations of vortices during ultracold-atom propagation through waveguides

Scattering in Quantum Tubes

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