Surface correlations for two-dimensional Coulomb fluids in a disc

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.Comment: 15 pages, Latex, submitted to J.Phys.:Condens.Matte

Lattice dynamics of anharmonic solids from first principles

An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated

A Generalization of the Stillinger-Lovett Sum Rules for the Two-Dimensional Jellium

In the equilibrium statistical mechanics of classical Coulomb fluids, the long-range tail of the Coulomb potential gives rise to the Stillinger-Lovett sum rules for the charge correlation functions. For the jellium model of mobile particles of charge $q$ immersed in a neutralizing background, the fixing of one of the $q$-charges induces a screening cloud of the charge density whose zeroth and second moments are determined just by the Stillinger-Lovett sum rules. In this paper, we generalize these sum rules to the screening cloud induced around a pointlike guest charge $Z q$ immersed in the bulk interior of the 2D jellium with the coupling constant $\Gamma=\beta q^2$ ($\beta$ is the inverse temperature), in the whole region of the thermodynamic stability of the guest charge $Z>-2/\Gamma$. The derivation is based on a mapping technique of the 2D jellium at the coupling $\Gamma$ = (even positive integer) onto a discrete 1D anticommuting-field theory; we assume that the final results remain valid for all real values of $\Gamma$ corresponding to the fluid regime. The generalized sum rules reproduce for arbitrary coupling $\Gamma$ the standard Z=1 and the trivial Z=0 results. They are also checked in the Debye-H\"uckel limit $\Gamma\to 0$ and at the free-fermion point $\Gamma=2$. The generalized second-moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space.Comment: 16 page

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear in Phys. Rev.

Finite N Fluctuation Formulas for Random Matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - )$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the circular random matrix ensemble the p.d.f.'s for the linear statistics ${1 \over 2} \sum_{j=1}^N (\theta_j - \pi)$ and $- \sum_{j=1}^N \log 2|\sin \theta_j/2|$ are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem as $N \to \infty$.Comment: LaTeX 2.09, 11 pages + 3 eps figs (needs epsf.sty

Two-dimensional one-component plasma on a Flamm's paraboloid

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Gamma=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations

The two-dimensional two-component plasma plus background on a sphere : Exact results

An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value $\Gamma = 2$ of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out~: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.Comment: 23 pages, Plain Te

Oscillons in dilaton-scalar theories

It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such "dilatonic" oscillons are already present in the simplest non-trivial DS theory -- a free massive scalar field coupled to the dilaton. It is shown that in analogy to the previously considered cases with a single nonlinear scalar field, in DS theories there are also time periodic quasibreathers (QB) associated to small amplitude oscillons. Exploiting the QB picture the radiation law of the small amplitude dilatonic oscillons is determined analytically.Comment: extended discussion on stability, to appear in JHEP, 29 pages, 7 figure

Classical Coulomb Systems:Screening and Correlations Revisited

From the laws of macroscopic electrostatics of conductors (in particular the existence of screening) taken for granted, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way for studying the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.Comment: 17 pages,TE

Cooperative Ring Exchange and Quantum Melting of Vortex Lattices in Atomic Bose-Einstein Condensates

Cooperative ring-exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly-rotating quasi two dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett. {\bf 56}, 873 (1986)] for the fractional quantized Hall effect, we calculate the condition for quantum melting instability by considering large-correlated ring exchanges in a two-dimensional Wigner crystal of vortices in a strong `pseudomagnetic field' generated by the background superfluid Bose particles. BEC may be profitably used to address issues of quantum melting of a pristine Wigner solid devoid of complications of real solids.Comment: 7 pages, 1 figure, to appear in Physical Review