Related papers: Resonances in a Dirichlet quantum waveguide couple…
We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues…
We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We…
In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths $\ell_\pm$ separated by a window of length 2a. It is known that if the barriers are semiinfinite,…
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling…
We consider curvature-induced resonances in a planar two-dimensional Dirichlet tube of a width $ d $. It is shown that the distances of the corresponding resonance poles from the real axis are exponentially small as $ d\to 0+ $, provided…
Interference of quasi bound states is studied in a ballistic electron ripple waveguide with two ripple cavities whose distance apart can be varied. This system is the waveguide analog of Dicke's model for two interacting atoms in a…
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2.…
We deal with the time-domain acoustic wave propagation in the presence of a subwavelength resonator given by a Minneart bubble. This bubble is small scaled and enjoys high contrasting mass density and bulk modulus. It is well known that,…
This paper presents numerical investigations of flow-acoustic resonances in deep and inclined cavities using wall-resolved large-eddy simulations. A cavity with $D/L = 2.632$ is subjected to ($M_\infty=0.2$ and $0.3$) at three inclination…
In this paper we consider embedded eigenvalues of a Schroedinger Hamiltonian in a waveguide induced by a symmetric perturbation. It is shown that these eigenvalues become unstable and turn into resonances after twisting of the waveguide.…
In this paper, we consider an open tube of diameter $\epsilon>0$, on the side of which a small hole of size $\epsilon^2$ is pierced. The resonances of this tube correspond to the eigenvalues of the Laplacian operator with homogeneous…
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional…
We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for…
A waveguide coincides with a strip having two narrows of diameter $\epsilon$. Electron motion is described by the Helmholtz equation with Dirichlet boundary condition. The part of waveguide between the narrows plays the role of resonator…
We study a three dimensional system of a rectangular-waveguide resonator with an inserted thin ferrite disk. The interplay of reflection and transmission at the disk interfaces together with material gyrotropy effect, gives rise to a rich…
We study a Schrodinger particle in an infinite spherical well with an oscillating wall. Parametric resonances emerge when the oscillation frequency is equal to the energy difference between two eigenstates of the static cavity. Whereas an…
The resonances for the Dirichlet and Neumann Laplacian are studied on compactly perturbed waveguides. An upper bound on the number of resonances near the physical plane is proven. In the absence of resonances, an upper bound is proven for…
We study the interplay between rotation and openness for mode coupling in wavelength-scale microcavities. In cavities deformed from a circular disk, the decay rates of a quasi-degenerate pair of resonances may cross or anti-cross with…
Whispering gallery mode (WGM) of resonance occurs when a traveling wave faces grazing reflection and confinement at the inner surface of a spherical cavity. Such a resonance was observed with micrometer sized liquid droplet and with light…
Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index $n>1$. The outer resonances can be verified as the resonances which survive only outside the cavity in the small…