575 research outputs found
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Diffusion in a Granular Fluid - Theory
Many important properties of granular fluids can be represented by a system
of hard spheres with inelastic collisions. Traditional methods of
nonequilibrium statistical mechanics are effective for analysis and description
of the inelastic case as well. This is illustrated here for diffusion of an
impurity particle in a fluid undergoing homogeneous cooling. An appropriate
scaling of the Liouville equation is described such that the homogeneous
cooling ensemble and associated time correlation functions map to those of a
stationary state. In this form the familiar methods of linear response can be
applied, leading to Green - Kubo and Einstein representations of diffusion in
terms of the velocity and mean square displacement correlation functions. These
correlation functions are evaluated approximately using a cumulant expansion
and from kinetic theory, providing the diffusion coefficient as a function of
the density and the restitution coefficients. Comparisons with results from
molecular dynamics simulation are given in the following companion paper
Center of mass and relative motion in time dependent density functional theory
It is shown that the exchange-correlation part of the action functional
in time-dependent density functional theory , where
is the time-dependent density, is invariant under the
transformation to an accelerated frame of reference , where is an arbitrary
function of time. This invariance implies that the exchange-correlation
potential in the Kohn-Sham equation transforms in the following manner:
. Some of the
approximate formulas that have been proposed for satisfy this exact
transformation property, others do not. Those which transform in the correct
manner automatically satisfy the ``harmonic potential theorem", i.e. the
separation of the center of mass motion for a system of interacting particles
in the presence of a harmonic external potential. A general method to generate
functionals which possess the correct symmetry is proposed
Collective edge modes in fractional quantum Hall systems
Over the past few years one of us (Murthy) in collaboration with R. Shankar
has developed an extended Hamiltonian formalism capable of describing the
ground state and low energy excitations in the fractional quantum Hall regime.
The Hamiltonian, expressed in terms of Composite Fermion operators,
incorporates all the nonperturbative features of the fractional Hall regime, so
that conventional many-body approximations such as Hartree-Fock and
time-dependent Hartree-Fock are applicable. We apply this formalism to develop
a microscopic theory of the collective edge modes in fractional quantum Hall
regime. We present the results for edge mode dispersions at principal filling
factors and for systems with unreconstructed edges. The
primary advantage of the method is that one works in the thermodynamic limit
right from the beginning, thus avoiding the finite-size effects which
ultimately limit exact diagonalization studies.Comment: 12 pages, 9 figures, See cond-mat/0303359 for related result
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
Microscopic Functional Integral Theory of Quantum Fluctuations in Double-Layer Quantum Hall Ferromagnets
We present a microscopic theory of zero-temperature order parameter and
pseudospin stiffness reduction due to quantum fluctuations in the ground state
of double-layer quantum Hall ferromagnets. Collective excitations in this
systems are properly described only when interactions in both direct and
exchange particle-hole channels are included. We employ a functional integral
approach which is able to account for both, and comment on its relation to
diagrammatic perturbation theory. We also discuss its relation to Gaussian
fluctuation approximations based on Hubbard-Stratonovich-transformation
representations of interactions in ferromagnets and superconductors. We derive
remarkably simple analytical expressions for the correlation energy,
renormalized order parameter and renormalized pseudospin stiffness.Comment: 15 pages, 5 figure
Effect of the Equivalence Between Topological and Electric Charge on the Magnetization of the Hall Ferromagnet
The dependence on temperature of the spin magnetization of a two-dimensional
electron gas at filling factor unity is studied. Using classical Monte Carlo
simulations we analyze the effect that the equivalence between topological and
electrical charge has on the the behavior of the magnetization. We find that at
intermediate temperatures the spin polarization increases in a thirty per cent
due to the Hartree interaction between charge fluctuations.Comment: 4 pages. Submitted to Phys.Rev.
Low energy excitations of double quantum dots in the lowest Landau level regime
We study the spectrum and magnetic properties of double quantum dots in the
lowest Landau level for different values of the hopping and Zeeman parameters
by means of exact diagonalization techniques in systems of N=6 and N=7
electrons and filling factor close to 2. We compare our results with those
obtained in double quantum layers and single quantum dots. The Kohn theorem is
also discussed.Comment: 23 pages, 4 figures, 1 table; references added; journal versio
Solitons in polarized double layer quantum Hall systems
A new manifestation of interlayer coherence in strongly polarized double
layer quantum Hall systems with total filling factor
in the presence of a small or zero tunneling is theoretically
predicted. It is shown that moving (for small tunneling) and spatially
localized (for zero tunneling) stable pseudospin solitons develop which could
be interpreted as mobile or static charge-density excitations.
The possibility of their experimental observation is also discussed.Comment: Phys. Rev. B (accepted
Shock-Like Dynamics of Inelastic Gases
We provide a simple physical picture which suggests that the asymptotic
dynamics of inelastic gases in one dimension is independent of the degree of
inelasticity. Statistical characteristics, including velocity fluctuations and
the velocity distribution are identical to those of a perfectly inelastic
sticky gas, which in turn is described by the inviscid Burgers equation.
Asymptotic predictions of this continuum theory, including the t^{-2/3}
temperature decay and the development of discontinuities in the velocity
profile, are verified numerically for inelastic gases.Comment: 4 pages, 5 figures, revte
- …