Related papers: Understanding excitons using spherical geometry
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…
Excitons, bound electron-hole pairs, are responsible for strong optical resonances near the bandgap in low-dimensional materials and wide-bandgap insulators. Although current ab initio methods can accurately determine exciton energies and…
The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean…
We analyse the local geometric structure of self-similar sets with open set condition through the study of the properties of a distinguished family of spherical neighbourhoods, the typical balls. We quantify the complexity of the local…
A theoretical model of resonant hyper-Raman scattering by an ensemble of spherical semiconductor quantum dots has been developed. The electronic intermediate states are described as Wannier-Mott excitons in the framework of the envelope…
We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering…
An alternate formalism is developed to determine the energy eigenvalues of quantum mechanical systems, confined within a rigid impenetrable spherical box of radius $r_0$, in the framework of Wentzel-Kramers-Brillouin (WKB) approximation.…
We briefly review our works for graviton and spherical graviton potentials in a plane-wave matrix model. To compute them, it is necessary to devise a configuration of the graviton solutions, since the plane-wave matrix model includes mass…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
We approach the biexciton Schr\"{o}dinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton-exciton interactions being treated according to the recently developed composite boson…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
Two-dimensional stacking fault defects embedded in a bulk crystal can provide a homogeneous trapping potential for carriers and excitons. Here we utilize state-of-the-art structural imaging coupled with density functional and effective-mass…
The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is…
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…
In this work we developed a new problem solution methodology of contact interaction of acoustic medium with resilient finite bodies of cylindrical form, based on application of boundary integral equations method in conjunction with series…
We apply the topological theory of symmetry indicators to interaction-induced exciton band structures in centrosymmetric semiconductors. Crucially, we distinguish between the topological invariants inherited from the underlying electron and…
We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…