Related papers: Equilibrium measures in the presence of weak ratio…
Equilibrium measures in the real axis in the presence of rational external fields are considered. These external fields are called rational since their derivatives are rational functions. We analyze the evolution of the equilibrium measure,…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
The main subject of this paper is equilibrium problems on an unbounded conductor $\Sigma$ of the complex plane in the presence of a weakly admissible external field. An admissible external field $Q$ on $\Sigma$ satisfies, along with other…
The aim of this paper is to provide a complete analysis of the Coulomb equilibrium problem in the euclidean space $\mathbb{R}^d$, $d\geq2$, associated to the kernel $1/|x|^{d-2}$, with a non-convex external field created by an…
We consider the equilibrium problem for an external background potential in weighted potential theory, and show that for a large class of background potentials there is a complementarity relationship between the measure solving the weighted…
The purpose of this work is twofold. First, we aim to extend for $0<s<1$ the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials…
Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set,…
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
It is a well-known conjecture in $\beta$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and…
We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium…
In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational…
Non equilibrium effective field theory is presented as an inhomogeneous field theory, using a formulation which is analogous to that of a gauge theory. This formulation underlines the importance of structural aspects of non-equilibrium,…
We study the possibility of the existence of the electric current, formed by massive electrons and positrons, flowing along an external magnetic field. The charged fermions are supposed to have nonzero anomalous magnetic moments and…
This paper establishes the existence of equilibrium in an economy with production and a continuum of consumers, each of whose incomplete and price-dependent preferences are defined on commodities they may consider deleterious, bads which…
We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the…
In this survey article, we review some results and conjectures related to orthogonal polynomials on Cantor sets. The main purpose of this paper is to emphasize the role of equilibrium measures in order to have a general theory of…
With the sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the equilibrium measure in the presence of an external field…
The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and…