Related papers: Localization of low-energy eigenfunctions in Seba …
We consider Laplacian eigenfunctions in circular, spherical and elliptical domains in order to discuss three kinds of high-frequency localization: whispering gallery modes, bouncing ball modes, and focusing modes. Although the existence of…
This paper is dedicated to the spectral analysis of the semiclassical purely magnetic Laplacian on the plane in the situation where the magnetic field $B$ vanishes nondegenerately on an open smooth curve $\Gamma$. We prove the existence of…
We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon…
We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are…
We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon…
The localization of waves in two-dimensional clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to find localized modes for…
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single…
We study the boundary localization phenomenon, known as whispering gallery modes, for weak solutions to semilinear Dirichlet eigenvalue problems in the unit ball $B_1 \subseteq \mathbb{R}^d$ ($d \geq 2$) of the form \[ \begin{cases} -\Delta…
In this paper, we use the method of invariant sets of descending flows to demonstrate the existence of multiple sign-changing solutions for a class of elliptic problems with zero Dirichlet boundary conditions. By combining Nehari manifold…
The deviation of the energy position of a delocalized state from the center of Landau level is studied in the framework of the Chalker-Coddington model. It is demonstrated that introducing a weak Landau level mixing results in a shift of…
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…
We investigate the existence of higher order topological localized modes in moir\'{e} lattices of bilayer elastic plates. Each plate has a hexagonal array of discrete resonators and one of the plates is rotated an angle ($21.78^\circ$)…
The spectra of Sinai microwave billiards and rectangular billiards with statistically distributed circular scatterers have been taken as a function of the position of one wall, and of one of the scatterers, respectively. Whereas in the…
The large lattice constant of Moire superlattice formed in twisted bilayer graphene for small twist enables observing the Landau levels splitting into Hofstadter butterflies in energy spectra for moderate magnetic field. This is expected…
We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the…
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a…
In this paper, we deal with an obstacle placement problem inside a disk, that can be formulated as an energy minimization problem with respect to the rotations of the obstacle about its center, with respect to the translations of the…
We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the operator becomes nonlocal and this requires a suitable…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one using the standard partial wave analysis developed for…