Related papers: Fixed points for one-dimensional particle system w…
This work contributes to the problem of determining effective interaction between asymmetrically (likely or oppositely) charged objects whose total charge is neutralized by mobile pointlike counter-ions of the same charge, the whole system…
The unique property of Coulomb interaction in strict one-dimensional (1D) system is revealed that the Coulomb repulsion energy of paired electrons is divergent. As consequences, electrons in 1D system can not doubly occupy the same spatial…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience…
The steady states of an antitone electric system are described by an antitone function with respect to the componentwise order. When this function is bounded from below by a positive vector, it has only one fixed point. This fixed point is…
Quantum systems in extreme conditions can exhibit universal behavior far from equilibrium associated to nonthermal fixed points with a wide range of topical applications from early-universe inflaton dynamics and heavy-ion collisions to…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
Non-Hermitian physics in open quantum many-body systems provides novel opportunities for the discovery of exotic quantum phenomena unexpected in Hermitian systems. A previous study of the non-Hermitian Kondo problem in ultracold atoms…
We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with…
In multicomponent systems with strong local interaction one can encounter some phenomena absent in the standard systems of statistical physics and other multicomponent systems. Namely, a system with $N$ components in the bounded volume of…
We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping…
Structural and thermodynamic properties of ionic fluids are related to those of a simpler ``mimic'' system with short ranged intermolecular interactions in a spatially varying effective field by use of Local Molecular Field (LMF) theory,…
We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…