Related papers: A formula for the edge density $\sqrt{n}$-correcti…
We study the partition function $$ Z_n = \int_{\mathbb{C}^n } \prod_{1 \le j<k \le n} |z_{j}-z_{k}|^{2} \prod_{j=1}^{n} |z_j|^{2c}\, e^{-n V(z_{j})}\frac{d^{2}z_{j}}{\pi}, $$ where $c>-1$ and $$ V(z)= |z|^{2d}-t(z^{d}+\overline{z}^{d}),…
The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
We prove several results for the Coulomb gas in any dimension $d \geq 2$ that follow from isotropic averaging, a transport method based on Newton's theorem. First, we prove a high-density Jancovici-Lebowitz-Manificat law, extending the…
We examine a Coulomb gas consisting of $n$ identical repelling point charges at an arbitrary inverse temperature $\beta$, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the…
We introduce and prove a maximum principle for a natural quantity related to the $k$-point correlation function of the classical one-component Coulomb gas. As an application, we show that the gas is confined to the droplet by a well-known…
We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\frac{1}{1-\tau^2}\big(|z|^2-\tau \text{Re } z^2\big)-2c\log|z-a|, $$ where $\tau\in[0,1)$, $c\ge0$, and $a\ge0$. In the regimes where…
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of…
The large $N$ asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensional Coulomb gas. However for the latter, it is most natural to…
We study a class of radially symmetric Coulomb gas ensembles at inverse temperature $\beta=2$, for which the droplet consists of a number of concentric annuli, having at least one bounded ``gap'' $G$, i.e., a connected component of the…
For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$.…
For a family of bond percolation models on Z^{2} that includes the Fortuin-Kasteleyn random cluster model, we consider properties of the ``droplet'' that results, in the percolating regime, from conditioning on the existence of an open dual…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
Based on the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts, simultaneous $\chi^{2}$ analyses are performed for elastic scattering and fusion cross section data…
The grand potential of a classical Coulomb system has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system : the massless Gaussian field. Here, the Coulomb system is assumed to be…
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the…
The large-$Z$ asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading $Z…
We obtain concentration estimates for the fluctuations of Coulomb gases in any dimension and in a broad temperature regime, including very small and very large temperature regimes which may depend on the number of points. We obtain a full…
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…
In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the $d$-dimensional cube $[-1,1]^d$ and an $L_q$-ball centred at the origin; this is clearly equivalent to approximating the distribution of…