38 research outputs found
Coulomb system equivalent to the energy spectrum of the Calogero-Sutherland-Moser (CSM) model
The purpose of this paper is to prove an equivalence between the energy spectrum of the CSM model and the electrostatic energy of a one-dimensional lattice of quantized point charges interacting via Coulomb potential with Dirichlet boundary condition
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
On the anomalous thermal conductivity of one-dimensional lattices
The divergence of the thermal conductivity in the thermodynamic limit is
thoroughly investigated. The divergence law is consistently determined with two
different numerical approaches based on equilibrium and non-equilibrium
simulations. A possible explanation in the framework of linear-response theory
is also presented, which traces back the physical origin of this anomaly to the
slow diffusion of the energy of long-wavelength Fourier modes. Finally, the
results of dynamical simulations are compared with the predictions of
mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics Letter
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
is computed exactly and shown to satisfy a central limit theorem as . For the circular random matrix ensemble the p.d.f.'s for the linear
statistics and 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 .Comment: LaTeX 2.09, 11 pages + 3 eps figs (needs epsf.sty
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
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 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
Collective modes and correlations in one-component plasmas
The static and time-dependent potential and surface charge correlations in a
plasma with a boundary are computed for different shapes of the boundary. The
case of a spheroidal or spherical one-component plasma is studied in detail
because experimental results are available for such systems. Also, since there
is some knowlegde both experimental and theoretical about the electrostatic
collective modes of these plasmas, the time-dependent correlations are computed
using a method involving these modes.Comment: 20 pages, plain TeX, submitted to Phys. Rev.
Screening of classical Casimir forces by electrolytes in semi-infinite geometries
We study the electrostatic Casimir effect and related phenomena in
equilibrium statistical mechanics of classical (non-quantum) charged fluids.
The prototype model consists of two identical dielectric slabs in empty space
(the pure Casimir effect) or in the presence of an electrolyte between the
slabs. In the latter case, it is generally believed that the long-ranged
Casimir force due to thermal fluctuations in the slabs is screened by the
electrolyte into some residual short-ranged force. The screening mechanism is
based on a "separation hypothesis": thermal fluctuations of the electrostatic
field in the slabs can be treated separately from the pure image effects of the
"inert" slabs on the electrolyte particles. In this paper, by using a
phenomenological approach under certain conditions, the separation hypothesis
is shown to be valid. The phenomenology is tested on a microscopic model in
which the conducting slabs and the electrolyte are modelled by the symmetric
Coulomb gases of point-like charges with different particle fugacities. The
model is solved in the high-temperature Debye-H\"uckel limit (in two and three
dimensions) and at the free fermion point of the Thirring representation of the
two-dimensional Coulomb gas. The Debye-H\"uckel theory of a Coulomb gas between
dielectric walls is also solved.Comment: 25 pages, 2 figure
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
Finite thermal conductivity in 1d lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing
that it is the first example of a 1d nonlinear lattice exhibiting normal
transport properties in the absence of an on-site potential. Numerical
estimates obtained by simulating a chain in contact with two thermal baths at
different temperatures are found to be consistent with those ones based on
linear response theory. The dynamics of the Fourier modes provides direct
evidence of energy diffusion. The finiteness of the conductivity is traced back
to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis
of two variants of this model.Comment: 4 pages, 3 postscript figure