论文标题
差距概率和一维单一组分等离子体中的完整计数统计数据
Gap probability and full counting statistics in the one dimensional one-component plasma
论文作者
论文摘要
我们考虑了热平衡中的$ 1D $一组分等离子体（OCP），由一条线上的$ n $相同的粒子组成，具有成对的库仑抑制，并受外部谐波电位的限制。我们研究了两个可观察到的东西：（i）在批量中两个连续的粒子之间的间隙分布，以及（ii）粒子数量$ n_i $在固定间隔$ i = [ - l，+l] $中的分布，批量内部，所谓的全计算统计数据（FCS）。对于两个可观察的物品，我们计算，对于$ n $，典型和非典型大波动的分布。我们表明，间隙的典型波动的分布由缩放表格$ {\ cal p} _ {\ rm gap，bulk}（g，n）\ sim nh_α（g，g \，n）$，其中$α$，其中$α$是互动coupling coupling coupling和缩放功能$h_α（z）$ $h_α（z）$计算。它比大$ z $的高斯尾巴更快：$h_α（z）\ sim e^{ - z^3/（96α）} $作为$ z \ to \ infty $。同样，对于FCS，我们表明$ n_i $的典型波动的分布由缩放表格$ {\ cal p} _ {\ rm fcs}（\ rm fcs}（n_i，n_i，n）\ sim2α\，u_i_α[2α（n_i- \ bar {n_i - \ bar {n n n} n $ {n y $ {wery = l \，n/（2α）$是$ n_i $的平均值，比例功能$u_α（z）$明确获得。对于这两种可观察到的东西，我们都表明，大波动的概率是由大偏差形式描述的，其速率函数我们明确地计算了。我们的数值蒙特卡洛模拟与我们的分析预测非常吻合。
We consider the $1d$ one-component plasma (OCP) in thermal equilibrium, consisting of $N$ equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We study two observables: (i) the distribution of the gap between two consecutive particles in the bulk and (ii) the distribution of the number of particles $N_I$ in a fixed interval $I=[-L,+L]$ inside the bulk, the so-called full-counting-statistics (FCS). For both observables, we compute, for large $N$, the distribution of the typical as well as atypical large fluctuations. We show that the distribution of the typical fluctuations of the gap are described by the scaling form ${\cal P}_{\rm gap, bulk}(g,N) \sim N H_α(g\,N)$, where $α$ is the interaction coupling and the scaling function $H_α(z)$ is computed explicitly. It has a faster than Gaussian tail for large $z$: $H_α(z) \sim e^{-z^3/(96 α)}$ as $z \to \infty$. Similarly, for the FCS, we show that the distribution of the typical fluctuations of $N_I$ is described by the scaling form ${\cal P}_{\rm FCS}(N_I,N) \sim 2α\, U_α[2 α(N_I - \bar{N}_I)]$, where $\bar{N}_I = L\,N/(2 α)$ is the average value of $N_I$ and the scaling function $U_α(z)$ is obtained explicitly. For both observables, we show that the probability of large fluctuations are described by large deviations forms with respective rate functions that we compute explicitly. Our numerical Monte-Carlo simulations are in good agreement with our analytical predictions.
