Related papers: Additive energy, discrepancy and Poissonian $k$-le…
By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…
In statistics, the Pearson correlation coefficient $r_{x,y}$ determines the degree of linear correlation between two variables and it is known that $-1 \le r_{x,y} \le 1$. In the theory of networks, a curious expression proposed in [PRL…
We consider the Energy-Energy Correlation (EEC) function in high-energy electron-positron annihilation to hadrons. In the back-to-back (two-jet) region, we perform the all-order resummation of the logarithmically-enhanced contributions in…
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit interval. Some effort has been made recently to…
We study the correlations of pairs of logarithms of positive integers at various scalings, either with trivial weigths or with weights given by the Euler function, proving the existence of pair correlation functions. We prove that at the…
We introduce a family of block-additive automatic sequences, that are obtained by allocating a weight to each couple of digits, and defining the $n$th term of the sequence as being the total weight of the integer $n$ written in base $k$.…
We continue our analysis of the number partitioning problem with $n$ weights chosen i.i.d. from some fixed probability distribution with density $\rho$. In Part I of this work, we established the so-called local REM conjecture of Bauke,…
The inflationary mechanism of mode amplification predicts that the state of each mode with a given wave vector is correlated to that of its partner mode with the opposite vector. This implies nonlocal correlations which leave their imprint…
Fix $\alpha,\theta >0$, and consider the sequence $(\alpha n^{\theta} \mod 1)_{n\ge 1}$. Since the seminal work of Rudnick--Sarnak (1998), and due to the Berry--Tabor conjecture in quantum chaos, the fine-scale properties of these dilated…
The third order correlation function of the scalar field advected by a Gaussian random velocity, with a spatial scaling exponent $2 - \epsilon$, and in the presence of a mean gradient, is calculated perturbatively in $\epsilon << 1$. This…
We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling…
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…
Local correlations of $2^+_1$ excitation energies and B(E2, $2^+_1\rightarrow \text{ g.s.}$) values require linear $N_pN_n$ systematics in a logarithmic scale, as confirmed by an experiment survey. Based on local correlations of…
Let $x(n):=\alpha n^d \mod 1$ for integer $d >1$ and non-zero real $\alpha$. We show that $\{x(n)\}_{n>0}$ has Poissonian $\ell$-point correlations for almost all choices of $\alpha$ when $d$ is large (depending on $\ell$). This falls in…
We present the computation of energy-energy correlation in $e^+e^-$ collisions in the back-to-back region at next-to-next-to-leading logarithmic accuracy matched with the next-to-next-to-leading order perturbative prediction. We study the…
Methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In one method, the electron density is…
Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinsky's model of two linearly coupled…