相关论文: Non-rigidity Properties of the Coulomb Gas
A random set of points in Euclidean space is called `rigid' or `hyperuniform' if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points.…
This article aims to study the Coulomb gas model over the $d$-dimensional $p$-adic space. We establish the existence of equilibria measures and the $\Gamma$-limit for the Coulomb energy functional when the number of configurations tends to…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an $L^1$ transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of…
The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against…
The model under consideration is the two-dimensional Coulomb gas of $\pm$ charged hard disks with diameter $\sigma$. For the case of pointlike charges $(\sigma=0)$, the system is stable against collapse of positive-negative pairs of charges…
For an inverse temperature $\beta>0$, we define the $\beta$-circular Riesz gas on $\mathbb{R}^d$ as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential $g(x) = \Vert x \Vert^{-s}$.…
We review what is known, unknown and expected about the mathematical properties of Coulomb and Riesz gases. Those describe infinite configurations of points in $\mathbb{R}^d$ interacting with the Riesz potential $\pm |x|^{-s}$ (resp.…
We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle…
We prove the existence of a liquid-gas phase transition for continuous Gibbs point process in $\mathbb{R}^d$ with Quermass interaction. The Hamiltonian we consider is a linear combination of the volume $\mathcal{V}$, the surface measure…
We systematically study the properties of a charged Coulomb Bose gas with dipole-dipole interactions in the weak coupling limit at both zero and finite temperatures using the Hartree-Fock-Bogoliubov approach. We numerically analyze the…
The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either…
The statistical mechanics of a two dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby…
Using the collective variables theory, we study the effect of competition between Coulomb and dispersion forces on the gas-liquid phase behaviour of a model ionic fluid, i.e. a charge-asymmetric primitive model with additional short-range…
We introduce and prove a maximum principle for a natural quantity related to the $k$-point correlation function of the classical one-component Coulomb gas. As an application, we show that the gas is confined to the droplet by a well-known…
We study the nonequilibrium steady state of a two dimensional Coulomb gas under the action of an anisotropic harmonic trapping potential along with a non-conservative rotational force. In the case without rotation, the equilibrium (zero…
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…
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and a pairwise repulsive…
The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size…
The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the…