Related papers: Potential theory with multivariate kernels
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
A new effective field theory has been developed to describe shallow $P$-wave resonances using nonlocal, momentum-dependent two-body potentials. This approach is expected to facilitate many-body calculations and has been demonstrated to…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular…
The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an…
We provide sufficient conditions for the solution of the classical inverse problem in the canonical distribution for multi-particle densities. Specifically, we show that there exists a unique potential in the form of a sum of m-particle (m…
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron scattering at low energies. We demonstrate that in attractive channels the…
A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a…
We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known $GW$ self-energy, as well as the particle-particle and electron-hole $T$-matrix self-energies. Each of these…
Inspired by the Thomson problem in physics where the distribution of multiple propelling electrons on a unit sphere can be modeled via minimizing some potential energy, hyperspherical energy minimization has demonstrated its potential in…
After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the Deformed Minkowski space lead…
In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…
We study effective three-particle interactions between valence electrons, which are induced by the core polarization. Such interactions are enhanced when valence orbitals have strong overlap with the outermost core shell, in particular for…
The potential energy curves for molecular ions up to $N_2^{4+}$ are calculated in an ab initio manner using the multi configurational self-consistent field method. Specifically, we implement in an automatic way a previously used double loop…
In condensed matter theory many invaluable models rely on the possibility of subsuming fundamental particle interactions in constitutive relations for macroscopic fields in near equilibrium assemblies of particles. Should one wish to…
We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exists curves in the…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
We present a unifying treatment of dark energy and modified gravity that allows distinct conformal-disformal couplings of matter species to the gravitational sector. In this very general approach, we derive the conditions to avoid ghost and…