Related papers: A generalized plasma and interpolation between cla…
Accurate "first-principle" expressions for the excess free energy $F_{ex}$ and internal energy $U_{ex}$ of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto…
An advance in experimental plasma diagnostics is presented and used to make the first measurement of a plasma velocity-space cross-correlation matrix. The velocity space correlation function can detect collective fluctuations of plasmas…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
In a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue p.d.f.'s are beta-generalizations of the classical…
We present large scale simulations of the diffusion constant $D$ of a random composite consisting of aligned platelets with aspect ratio $a/b>>1$ in a matrix (with diffusion constant $D_0$) and find that $D/D_0 = 1/(1+ c_1 x + c_2 x^2)$,…
In a layered and strongly anisotropic superconductor the hybrid modes provided by the propagation of electromagnetic waves in the matter identify two well separate energy scales connected to the large in-plane plasma frequency and to the…
It is well-known that the partition function of the unitary ensembles of random matrices is given by a tau-function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are tau-functions of the Pfaff lattice…
The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF),…
The two-dimensional one-component plasma ---2dOCP--- is a system composed by $n$ mobile particles with charge $q$ over a neutralizing background in a two-dimensional surface. The Boltzmann factor of this system, at temperature $T$, takes…
Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…
We study the behavior of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions…
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread…
We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…
It is shown that a wide range of probabilities and limiting probabilities in finite classical groups have integral coefficients when expanded as a power series in 1/q. Moreover it is proved that the coefficients of the limiting…
The universal finite-size correction to the free energy of a two-dimensional Coulomb system is checked in the special case of a one-component plasma on a sphere. The correction is related to the known second moment of the short-range part…
In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such…
We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…
The model under consideration is a two-dimensional two-component plasma, i.e., a continuous system of two species of pointlike particles of opposite charges $\pm 1$, interacting through the logarithmic Coulomb interaction. Using the exact…
We derive the exact longitudinal plasmon dispersion relations, $\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…