Truncated linear statistics in the one dimensional one-component plasma
نویسندگان
چکیده
In this paper, we study the probability distribution of observable $s = (1/N)\sum_{i=N-N'+1}^N x_i$, with $1 \leq N' N$ and $x_1<x_2<\cdots< x_N$ representing ordered positions $N$ particles in a $1d$ one-component plasma, i.e., harmonically confined charges on line, pairwise repulsive Coulomb interaction $|x_i-x_j|$. This represents an example truncated linear statistics -- here center mass $N' \kappa \, (with $0 < 1$) rightmost particles. It interpolates between position particle (in limit $\kappa \to 0$) full 1$). We show that, for large $N$, $s$ fluctuates around its mean $\langle s \rangle$ typical fluctuations are Gaussian, width $O(N^{-3/2})$. The atypical $s$, fixed $\kappa$, instead described by deviation form ${\cal P}_{N, \kappa}(s)\simeq \exp{\left[-N^3 \phi_\kappa(s)\right]}$, where rate function $\phi_\kappa(s)$ is computed analytically. that $\phi_{\kappa}(s)$ takes different functional forms five distinct regions $(\kappa,s)$ plane separated phase boundaries, thus leading to rich diagram plane. Across all boundaries $\phi(\kappa,s)$ undergoes third-order transition. also evaluated numerically using sophisticated importance sampling method, find perfect agreement our analytical predictions.
منابع مشابه
Charge Fluctuations in the Two-Dimensional One-Component Plasma
We study, via computer simulations, the fluctuations in the net electric charge, in a two dimensional one component plasma (OCP) with uniform background charge density −eρ, in a region Λ inside a much larger overall neutral system. Setting e = 1 this is the same as the fluctuations in NΛ, the number of mobile particles of charge e. As expected the distribution of NΛ has, for large Λ, a Gaussian...
متن کاملIs the Two-Dimensional One-Component Plasma Exactly Solvable?
The model under consideration is the two-dimensional (2D) one-component plasma of pointlike charged particles in a uniform neutralizing background, interacting through the logarithmic Coulomb interaction. Classical equilibrium statistical mechanics is studied by non-traditional means. The question of the potential integrability (exact solvability) of the plasma is investigated, first at arbitra...
متن کاملThe one-component plasma: a conceptual approach
The one-component plasma (OCP) represents the simplest statistical mechanical model of a Coulomb system. For this reason, it has been extensively studied over the last forty years. The advent of the integral equations has resulted in a dramatic improvement in our ability to carry out numerical calculations, but came at the expense of a physical insight gained in a simpler analytic theory. In th...
متن کاملONE-DIMENSIONAL TREATMENT OF HYDROGEN BOND PART1 THE CASE OF THE LINEAR HYDROGENBOND
The one-dimensional model of Lippincott and Schroeder for hydrogen bond has Been re-examined and it has been shown that O-H bond distance depends on repulsive van der Waals and attractive electrostatic potentials.it has been shown that constant b in the van der Waals repulsion potential is not transferable to all hydrogen bonds. The possibility of obtaining the semi-empircal parameters i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A
سال: 2021
ISSN: ['1751-8113', '1751-8121']
DOI: https://doi.org/10.1088/1751-8121/ac2599