Addendum to P. Exner, E.M. Harrell, M. Loss: Inequalities for means of chords, with application to isoperimetric problems, Lett. Math. Phys. 75 (2006), 225–233

Exner, Pavel; Harrell, Evans M.; Loss, Michael

doi:10.1007/s11005-006-0087-1

Cited by 44 publications

(64 citation statements)

References 3 publications

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“…It is known that for the field-free case, excited bound states exist at the wide enough opening only; for example, at the equal widths, d 1 = d 2 = 1, the second Q1D localized level with its odd wavefunction emerges from the continuum at s cr 1 = 1.447 whereas the next symmetric orbital is observed at the lengths greater than s cr 2 = 2.560, etc. 34 For the 3D geometry, ground state is cylindrically symmetric, m = 0, while the second level with |m| = 1 exists at the diameter not smaller than 2.054 and is followed by |m| = 2 orbital with s cr = 3.098 and another m = 0 state with its critical diameter being equal to 3.132. 50 Applied voltage destroys a transverse symmetry of the structure leading in this way to the changes of the critical widths s crn .…”

Section: Resultsmentioning

confidence: 96%

Electric-field control of bound states and optical spectrum in window-coupled quantum waveguides

Olendski

2018

Journal of Applied Physics

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Properties of the bound states of two quantum waveguides coupled via the window of the width s in their common boundary are calculated under the assumption that the transverse electric field E E E is applied to the structure. It is shown that the increase of the electric intensity brings closer to each other fundamental propagation thresholds of the opening and the arms. As a result, the ground state, which in the absence of the field exists at any nonzero s, exhibits the energy E 0 decrease for the growing E and in the high-field regime E 0 stays practically the same regardless of the size of the connecting region. It is predicted that the critical window widths s crn , n = 1, 2, . . ., at which new excited localized orbitals emerge, strongly depend on the transverse voltage; in particular, the field leads to the increase in s crn , and, for quite strong electric intensities, the critical width unrestrictedly diverges. This remarkable feature of the electric-field-induced switching of the bound states can be checked, for example, by the change of the optical properties of the structure when the gate voltage is applied; namely, both the oscillator strength and absorption spectrum exhibit a conspicuous maximum on their E dependence and turn to zero when the electric intensity reaches its critical value. Comparative analysis of the two-dimensional (2D) and 3D geometries reveals their qualitative similarity and quantitative differences. a) Electronic address: oolendski@sharjah.ac.ae

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Section: Resultsmentioning

confidence: 96%

Electric-field control of bound states and optical spectrum in window-coupled quantum waveguides

Olendski

2018

Journal of Applied Physics

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“…Furthermore, the length l d is the total length L d , divided by the repetition number in the case that the diffractive orbit is a multiple repetition of a shorter one. The diffraction coefficient is D, which for a point scatterer is independent of incoming and outgoing angles and given by [18,33] …”

Section: Short-wave Approximationmentioning

confidence: 99%

Trace formula for a dielectric microdisk with a point scatterer

Hales¹,

Sieber²,

Waalkens³

2011

J. Phys. A: Math. Theor.

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Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.

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“…Another possibility is to relax the regularity requirement to solution φ to a twodimensional Helmholtz equation at the junction points. This approach is formally equivalent to the limit r → 0 and is described in [19], [20], [21] and [22]. However since we are interested in global structures that extend over the whole graph (billiard) the detail character of the connection is not important.…”

Section: Fig 2: Nodal Domains An Eigenfunctionmentioning

confidence: 99%

Approximations by graphs and emergence of global structures

Exner

Hejcik

Šeba

2006

Reports on Mathematical Physics

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We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schrödinger equation with energy rescaled by the billiard dimension.As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.

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Addendum to P. Exner, E.M. Harrell, M. Loss: Inequalities for means of chords, with application to isoperimetric problems, Lett. Math. Phys. 75 (2006), 225–233

Cited by 44 publications

References 3 publications

Electric-field control of bound states and optical spectrum in window-coupled quantum waveguides

Electric-field control of bound states and optical spectrum in window-coupled quantum waveguides

Trace formula for a dielectric microdisk with a point scatterer

Approximations by graphs and emergence of global structures

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