相关论文: Resonance widths for general Helmholtz Resonators …
The confinement properties of the open structure formed crossing a circular waveguide perpendicular to a parallel-plate waveguide are discussed, highlighting the fundamental differences with respect to the common high-frequency resonators.…
Let $\Lambda\subset \mathbb{R}^d$ be a domain consisting of several cylinders attached to a bounded center. One says that $\Lambda$ admits a threshold resonance if there exists a non-trivial bounded function $u$ solving $-\Delta u=\nu u$ in…
The aim of this short note is to show how to construct a rationnal Remmert reduction for the universal cover of a smooth K\"ahler orbifold. Doins this, we are led to introduce some singular K\"ahler metrics adapted to the orbifold…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
In this paper, we give some bounds for principal eigenvector and spectral radius of connected uniform hypergraphs in terms of vertex degrees, the diameter, and the number of vertices and edges.
Higgs resonance modes in condensed matter systems are generally broad; meaning large decay widths or short relaxation times. This common feature has obscured and limited their observation to a select few systems. Contrary to this, the…
For $h$-FEM discretisations of the Helmholtz equation with wavenumber $k$, we obtain $k$-explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbin 1991], [Demlow, Guzm\'an, Schatz 2011], showing that these…
The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together.…
We investigate the simple resonances of a 2 by 2 matrix of n-dimensional semiclassical Shr\"odinger operators that interact through a first order differential operator. We assume that one of the two (analytic) potentials admits a well with…
We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyse both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by…
Circular microresonators (microdisks) are micron sized dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental…
On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex…
We consider the large $L$ limit of one dimensional Schr\"odinger operators $H_L=-d^2/dx^2 + V_1(x) + V_{2,L}(x)$ in two cases: when $V_{2,L}(x)=V_2(x-L)$ and when $V_{2,L}(x)=e^{-cL}\delta(x-L)$. This is motivated by some recent work of…
Extending the cavity length of diode lasers with feedback from Bragg structures and ring resonators is highly effective for obtaining ultra-narrow laser linewidths. However, cavity length extension also decreases the free-spectral range of…
We discuss the relationship between the zero modes of electromagnetic fields in a cavity resonator and the cavity's topological characteristics. We show that the dimension of the electromagnetic zero-mode space coincides with the dimension…
We discuss the resonances of Hamiltonians with constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for…
A Gelfand triplet for the Hamiltonian H of the infinite-dimensional Friedrichs model on the positive half line with Hilbert-Schmidt perturbations is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix)…
Unidirectional radiation is important for a variety of optoelectronic applications. Many unidirectional emitters exist, but they all rely on the use of materials or structures that forbid outgoing waves, i.e. mirrors. Here, we theoretically…
We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the…