Related papers: Ringing the eigenmodes from compact manifolds
We make a computational study to know what kind of isospectralities among lens spaces and lens orbifolds exist considering the Hodge--Laplace operators acting on smooth $p$-forms. Several evidenced facts are proved and some others are…
We introduce a new technique to the study and identification of submanifolds of simply-connected symmetric spaces of compact type based upon an approach computing $k$-positive Ricci curvature of the ambient manifolds and using this…
In this paper we set up a general formalism to deal with quantum theories on a Lobatchevski space, i.e. a spatial manifold that is homogeneous, isotropic and has negative curvature. The heart of our approach is the construction of a…
We give various estimates of the first eigenvalue of the $p$-Laplace operator on closed Riemannian manifold with integral curvature conditions.
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…
Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…
We study numerically the eigenmode spectrum of the covariant lattice Laplacian, in the fundamental SU(2) color group representation. It is found that eigenmodes at the lower and upper ends of the spectrum are localized, and that the…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
In this paper we investigate estimates about the Laplace operator in heat flows of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain…
We compute the Euler-Poincar\'e characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.
Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal…
Flatbands play an important role in correlated quantum matter and have novel applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such…
We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem…
We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge…
This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail, including flip algorithms. The Laplacian…
We consider a family of compact, oriented and connected Riemannian manifolds shrinking to a metric graph and describe the asymptotic behaviour of the eigenvalues of the Hodge Laplacian. We apply our results to produce manifolds with…
We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for…
A numerical approach is proposed for studying the quantum optical modes in the Klein-Gordon lattices where the energy contribution of the atomic displacements is non-quadratic. The features of the biphonon excitations are investigated in…
Cavities, because they trap waves for long times due to their reflecting walls, are used in a vast number of scientific domains. Indeed, in these closed media and due to interferences, the free space continuum of solutions becomes a…
In this work we introduce a new method for manufacturing minimal submanifolds in Riemannian geometry. For this we employ the so called complex-valued eigenfunctions. This is particularly interesting in the cases when the Riemannian ambient…