Related papers: Loi de Weyl presque sure pour un systeme different…

We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the…

Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here we show that typical resonances in generic open quantum systems follow a modified,…

In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…

In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many…

In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…

Weyl semimetal is a three-dimensional material with a conical spectrum near an even number of point nodes, where two bands touch each other. Here we study spectral properties of surface electron states in such a system. We show that the…

We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…

Let $G$ be a 1-connected, almost-simple Lie group over a local field and $\mathcal{S}$ a subsemigroup of $G$ with non-empty interior. The action of the regular hyperbolic elements in the interior of $\mathcal{S}$ on the flag manifold $G/P$…

A classical theorem of Weyl states that any polynomial with an irrational coefficient other than the constant term is uniformly distributed mod 1. We prove a new function field analogue of this statement, confirming a conjecture of L\^{e},…

A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasi-characteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner…

Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\mu_\mathcal{X}$. Then, the spectrum of…

We construct explicit families of graphs whose eigenvalues are asymptotically distributed according to Wigner's semicircle law; in other words, that are spectrally indistinguishable from random graphs. However, in other respects they are…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of…

We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…

We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ in which the upper triangular entries are independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E…

Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties.…

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V,\ V\ge 0,$ we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues (bound states), as the coupling parameter $\alpha$ tends to infinity.…

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (-d^2/dx^2)^(alpha/2) (0 < alpha < 2) in the interval (-1,1) is given: the n-th eigenvalue is equal to (n pi/2 - (2 - alpha) pi/8)^alpha +…

We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…