Related papers: Sharp stability for the interaction energy
We study the relationship between universal effects and the Coulomb interaction. Here, we present our approach and a first illustrative example. Understanding the relationship of universality and the Coulomb interaction is important for…
We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative $N$-particle system, obtained by passing to the grazing limit on Kac's walk in his program for the Boltzmann equation. Our…
Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response…
We consider the two-dimensional Coulomb gas with a general potential at the determinantal temperature, or equivalently, the eigenvalues of random normal matrices. We prove that the smallest gaps between particles are typically of order…
A tight binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the Density Matrix Renormalization Group method which we prove applicable also to very long range potentials. From the analysis…
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…
We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The…
A method is proposed for estimating the potential function of a non-parametric estimator for stationary and isotropic pairwise interaction point process. The relation between a pair potential and the corresponding Papangelou conditional…
The resistance coefficients in screen Coulomb potential of stellar plasma are evaluated in high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of…
This paper presents a qualitative explanation for the hollowness effect based on the inelastic overlap function, claiming this result is a consequence of fundamental thermodynamic processes. Using the Tsallis entropy, one identifies the…
The interacting dark energy model could propose a effective way to avoid the coincidence problem. In this paper, dark energy is taken as a fluid with a constant equation of state parameter $w_x$. In a general gauge, we could obtain two sets…
Recently there have been several proposals of materials predicted to be nodal-ring semimetals, where zero energy excitations are characterized by a nodal ring in the momentum space. This class of materials falls between the Dirac-like…
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix given by the convolution product of the solution with the…
We investigate the structure and stability of Bose-Einstein condensate of $^{7}$Li atoms with realistic van der Waals interaction by using the potential harmonic expansion method. Besides the known low-density metastable solution with…
Using a combination of Kawashima- and Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems. This extends previous results obtained by Plaza and Zumbrun…
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…
The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant $\ew$ are studied from the first Born-Green-Yvon equation combined with…
To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U_00 =…
This article extends the previous paper in "M.W. Yuen, \textit{Stabilities for Euler-Poisson Equations in Some Special Dimensions}, J. Math. Anal. Appl. \textbf{344} (2008), no. 1, 145--156.", from the Euler-Poisson equations for attractive…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…