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We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension…
The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning…
Truss structures at macro-scale are common in a number of engineering applications and are now being increasingly used at the micro-scale to construct metamaterials. In analyzing the properties of a given truss structure, it is often…
The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…
We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson…
The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. The spectrum of the Laplacian on the unperturbed graph is a union of a finite number…
In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincar\'e series equipped with the polyhedral…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and time-periodic velocity field, we prove that all sufficiently…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in $\mathbb{R}^3$ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional…
Spectral gaps play a fundamental role in many areas of mathematics, computer science, and physics. In quantum mechanics, the spectral gap of Schr\"odinger operators has a long history of study due to its physical relevance, while in quantum…