294 research outputs found
Linear Response for Confined Particles
The dynamics of fluctuations is considered for electrons near a positive ion
or for charges in a confining trap. The stationary nonuniform equilibrium
densities are discussed and contrasted. The linear response function for small
perturbations of this nonuniform state is calculated from a linear Markov
kinetic theory whose generator for the dynamics is exact in the short time
limit. The kinetic equation is solved in terms of an effective mean field
single particle dynamics determined by the local density and dynamical
screening by a dielectric function for the non-uniform system. The
autocorrelation function for the total force on the charges is discussed.Comment: 4 pages, 1 figure. Results presented at the "International Conference
on Strongly Coupled Coulomb Systems", Camerino, Italy, July 2008. Submitted
for publication in the conference proceedings (special issue of Journal of
Physics A
Transport Far From Equilibrium --- Uniform Shear Flow
The BGK model kinetic equation is applied to spatially inhomogeneous states
near steady uniform shear flow. The shear rate of the reference steady state
can be large so the states considered include those very far from equilibrium.
The single particle distribution function is calculated exactly to first order
in the deviations of the hydrodynamic field gradients from their values in the
reference state. The corresponding non-linear hydrodynamic equaitons are
obtained and the set of transport coefficients are identified as explicit
functions of the shear rate. The spectrum of the linear hydrodynamic equation
is studied in detail and qualitative differences from the spectrum for
equilibrium fluctuations are discussed. Conditions for instabilities at long
wavelengths are identified and disccused.Comment: 32 pages, 1 figure, RevTeX, submitted to Phys. Rev.
Nonlinear response of electrons to a positive ion
Electric field dynamics at a positive ion imbedded in an electron gas is
considered using a semiclassical description. The dependence of the field
autocorrelation function on charge number is studied for strong ion-electron
coupling via MD simulation. The qualitative features for larger charge numbers
are a decreasing correlation time followed by an increasing anticorrelation.
Stopping power and related transport coefficients determined by the time
integral of this correlation function result from the competing effects of
increasing initial correlations and decreasing dynamical correlations. An
interpretation of the MD results is obtained from an effective single particle
model showing good agreement with the simulation results.Comment: To be published in the proceedings of the International Workshop on
Strongly Coupled Coulomb Systems, Journal of Physics
Kinetic Theory for Electron Dynamics Near a Positive Ion
A theoretical description of time correlation functions for electron
properties in the presence of a positive ion of charge number Z is given. The
simplest case of an electron gas distorted by a single ion is considered. A
semi-classical representation with a regularized electron - ion potential is
used to obtain a linear kinetic theory that is asymptotically exact at short
times. This Markovian approximation includes all initial (equilibrium) electron
- electron and electron - ion correlations through renormalized pair
potentials. The kinetic theory is solved in terms of single particle
trajectories of the electron - ion potential and a dielectric function for the
inhomogeneous electron gas. The results are illustrated by a calculation of the
autocorrelation function for the electron field at the ion. The dependence on
charge number Z is shown to be dominated by the bound states of the effective
electron - ion potential. On this basis, a very simple practical representation
of the trajectories is proposed and shown to be accurate over a wide range
including strong electron - ion coupling. This simple representation is then
used for a brief analysis of the dielectric function for the inhomogeneous
electron gas.Comment: 30 pages, 5 figures, submitted to Journal of Statistical Mechanics:
Theory and Experimen
Stability of Uniform Shear Flow
The stability of idealized shear flow at long wavelengths is studied in
detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for
small shear rates is given to identify the origin and universality of an
instability at any finite shear rate for sufficiently long wavelength
perturbations. The analysis is extended to larger shear rates using a low
density model kinetic equation. Direct Monte Carlo Simulation of this equation
is computed with a hydrodynamic description including non Newtonian rheological
effects. The hydrodynamic description of the instability is in good agreement
with the direct Monte Carlo simulation for , where is the mean
free time. Longer time simulations up to are used to identify the
asymptotic state as a spatially non-uniform quasi-stationary state. Finally,
preliminary results from molecular dynamics simulation showing the instability
are presented and discussed.Comment: 25 pages, 9 figures (Fig.8 is available on request) RevTeX, submitted
to Phys. Rev.
Long Wavelength Instability for Uniform Shear Flow
Uniform Shear Flow is a prototype nonequilibrium state admitting detailed
study at both the macroscopic and microscopic levels via theory and computer
simulation. It is shown that the hydrodynamic equations for this state have a
long wavelength instability. This result is obtained first from the
Navier-Stokes equations and shown to apply at both low and high densities.
Next, higher order rheological effects are included using a model kinetic
theory. The results are compared favorably to those from Monte Carlo
simulation.Comment: 12 pages, including 2 figure
Theoretical Description of Coulomb Balls - Fluid Phase
A theoretical description for the radial density profile of a finite number
of identical charged particles confined in a harmonic trap is developed for
application over a wide range of Coulomb coupling (or, equivalently,
temperatures) and particle numbers. A simple mean field approximation
neglecting correlations yields a density profile which is monotonically
decreasing with radius for all temperatures, in contrast to molecular dynamics
simulations and experiments showing shell structure at lower temperatures. A
more complete theoretical description including charge correlations is
developed here by an extension of the hypernetted chain approximation,
developed for bulk fluids, to the confined charges. The results reproduce all
of the qualitative features observed in molecular dynamics simulations and
experiments. These predictions are then tested quantitatively by comparison
with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory
is obtained for the selected conditions by correcting the hypernetted chain
approximation with a representation for the associated bridge functions.Comment: 10 figures, submitted to Physical Review
- …