Related papers: The Newtonian kernel at the intersection of two di…
Compact analytical forms are derived for the interactions involving thin disks in two dimensions using an integration approach. These include interactions between a disk and a material point, between two disks, and between a disk and a…
We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of $\hbar$. The phase space is enlarged to include a variable related to the…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
We provide a general treatment of perturbations of a class of functionals modeled on convolution energies with integrable kernel which approximate the $p$-th norm of the gradient as the kernel is scaled by letting a small parameter…
We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping…
Convolution is an essential operation in signal and image processing and consumes most of the computing power in convolutional neural networks. Photonic convolution has the promise of addressing computational bottlenecks and outperforming…
We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding…
The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…
A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable:…
An effect of overlapping of exhausted regions around droplets of a new phase is analyzed. Several approximation to take overlapping into account are suggested. The small parameter responsible for convergence is extracted. The multi particle…
In the theory of resonant scattering, the double differential cross section involves the computation of a multifold integral of a 4-point correlation function, which generalizes the traditional 2-point correlation function of Van-Hove for…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…
This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
We find the numerically exact partition potential for 1-D systems of interacting electrons designed to model diatomic molecules. At integer fragment occupations, the kinetic contribution to the partition potential develops sharp features in…
The Newtonian potential operator for the Helmholtz equation, which is represented by the volume integral with fundamental solution as kernel function, is of great importance for direct and inverse scattering of acoustic waves. In this…