Related papers: Minimization of the discrete interaction energy wi…
We investigate the spectral properties of a quasi-one-dimensional lattice in two possible dimerisation configurations. Both configurations are characterized by the same lattice topology and the identical spectra containing a flat band at…
We utilize an effective field theory approach to calculate Casimir interactions between objects bound to thermally fluctuating fluid surfaces or interfaces. This approach circumvents the complicated constraints imposed by such objects on…
Pairs potential-density in terms of elementary functions that represents flat rings structures are presented. We study structures representing one or several concentric flat rings. Also disks surrounded by concentric flat rings are…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
In this paper we characterise the minimisers of a one-parameter family of nonlocal and anisotropic energies $I_\alpha$ defined on probability measures in $\R^n$, with $n\geq 3$. The energy $I_\alpha$ consists of a purely nonlocal term of…
In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the…
Combining a brilliant obserbation of A. Tumanov with our computational approach to Thomson's 5-electron problem, we prove that the triangular bi-pyramid is the unique global minimizer for the Rieze potential R_s(r) = sign(s) r^{-s} amongst…
Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types…
The pair correlation function of a strongly interacting one-dimensional quantum dot is evaluated analytically within the framework of the spin coherent Luttinger liquid model. The influence of electron interactions and temperature on the…
In this paper we consider nonlocal energies defined on probability measures in the plane, given by a convolution interaction term plus a quadratic confinement. The interaction kernel is $-\log|z|+\alpha\, x^2/|z|^2, \; z=x+iy,$ with $-1 <…
We study existence and qualitative properties of the minimizers for a Thomas--Fermi type energy functional defined by $$E_\alpha(\rho):=\frac{1}{q}\int_{\mathbb{R}^d}|\rho(x)|^q…
We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex.…
An open problem in machine learning is whether flat minima generalize better and how to compute such minima efficiently. This is a very challenging problem. As a first step towards understanding this question we formalize it as an…
We derive and use an extremely simplified formula for the interaction Casimir energy for two separate bodies in the weak coupling regime for massless scalar fields. We derive closed form solutions for a general arrangement of two…
In the multi-component configurations of dark matter phenomenology, we propose a minimal two-component configuration which is an extension of the Standard Model with only three new fields; one scalar and one fermion interact with the…
In our model, spinless fermions (or hardcore bosons) on a square lattice hop to nearest neighbor sites, and also experience a hard-core repulsion at the nearest neighbor separation. This is the simplest model of correlated electrons and is…
A continuous system of moment equations is introduced that models the transverse dynamics of a beam of charged particles as it passes through an arbitrary lattice of quadrupoles and solenoids in the presence of self-fields. Then, figures of…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
We have calculated dynamical Casimir-Polder interaction force between a moving ground state atom and a flat polarizable surface. The velocity of an atom can be close to the velocity of light. The material properties are taken into account…
We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has…