808 research outputs found
Dielectric Function of Diluted Magnetic Semiconductors in the Infrared Regime
We present a study of the dielectric function of metallic (III,Mn)V diluted
magnetic semiconductors in the infrared regime. Our theoretical approach is
based on the kinetic exchange model for carrier induced (III,Mn)V
ferromagnetism. The dielectric function is calculated within the random phase
approximation and, within this metallic regime, we treat disorder effects
perturbatively and thermal effects within the mean field approximation. We also
discuss the implications of this calculations on carrier concentration
measurements from the optical f-sum rule and the analysis of plasmon-phonon
coupled modes in Raman spectra.Comment: 6 pages, 6 figures include
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
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
Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles
The presence of the aging phenomenon in the homogeneous cooling state (HCS)
of a granular fluid composed of inelastic hard spheres or disks is
investigated. As a consequence of the scaling property of the -particle
distribution function, it is obtained that the decay of the normalized two-time
correlation functions slows down as the time elapsed since the beginning of the
measurement increases. This result is confirmed by molecular dynamics
simulations for the particular case of the total energy of the system. The
agreement is also quantitative in the low density limit, for which an explicit
analytical form of the time correlation function has been derived. The reported
results also provide support for the existence of the HCS as a solution of the
N-particle Liouville equation.Comment: 17 pages, 3 figures; v3 revised version (minor changes, corrected
typos, v2=v1 due to a submission error)accepted for publication in J. Phys.
A: Math. Theo
Steady state representation of the homogeneous cooling state of a granular gas
The properties of a dilute granular gas in the homogeneous cooling state are
mapped to those of a stationary state by means of a change in the time scale
that does not involve any internal property of the system. The new
representation is closely related with a general property of the granular
temperature in the long time limit. The physical and practical implications of
the mapping are discussed. In particular, simulation results obtained by the
direct simulation Monte Carlo method applied to the scaled dynamics are
reported. This includes ensemble averages and also the velocity autocorrelation
function, as well as the self-diffusion coefficient obtained from the latter by
means of the Green-Kubo representation. In all cases, the obtained results are
compared with theoretical predictions
Granular Brownian motion
We study the stochastic motion of an intruder in a dilute driven granular
gas. All particles are coupled to a thermostat, representing the external
energy source, which is the sum of random forces and a viscous drag. The
dynamics of the intruder, in the large mass limit, is well described by a
linear Langevin equation, combining the effects of the external bath and of the
"granular bath". The drag and diffusion coefficients are calculated under few
assumptions, whose validity is well verified in numerical simulations. We also
discuss the non-equilibrium properties of the intruder dynamics, as well as the
corrections due to finite packing fraction or finite intruder mass.Comment: 19 pages, 4 figures, in press on Journal of Statistical Mechanics:
Theory and Experiment
Patterns and Long Range Correlations in Idealized Granular Flows
An initially homogeneous freely evolving fluid of inelastic hard spheres
develops inhomogeneities in the flow field (vortices) and in the density field
(clusters), driven by unstable fluctuations. Their spatial correlations, as
measured in molecular dynamics simulations, exhibit long range correlations;
the mean vortex diameter grows as the square root of time; there occur
transitions to macroscopic shearing states, etc.
The Cahn--Hilliard theory of spinodal decomposition offers a qualitative
understanding and quantitative estimates of the observed phenomena. When
intrinsic length scales are of the order of the system size, effects of
physical boundaries and periodic boundaries (finite size effects in
simulations) are important.Comment: 13 pages with 7 postscript figures, LaTeX (uses psfig). Submitted to
International Journal of Modern Physics
Evidence of a Critical time in Constrained Kinetic Ising models
We study the relaxational dynamics of the one-spin facilitated Ising model
introduced by Fredrickson and Andersen. We show the existence of a critical
time which separates an initial regime in which the relaxation is exponentially
fast and aging is absent from a regime in which relaxation becomes slow and
aging effects are present. The presence of this fast exponential process and
its associated critical time is in agreement with some recent experimental
results on fragile glasses.Comment: 20 Pages + 7 Figures, Revte
Noise Rectification and Fluctuations of an Asymmetric Inelastic Piston
We consider a massive inelastic piston, whose opposite faces have different
coefficients of restitution, moving under the action of an infinitely dilute
gas of hard disks maintained at a fixed temperature. The dynamics of the piston
is Markovian and obeys a continuous Master Equation: however, the asymmetry of
restitution coefficients induces a violation of detailed balance and a net
drift of the piston, as in a Brownian ratchet. Numerical investigations of such
non-equilibrium stationary state show that the velocity fluctuations of the
piston are symmetric around the mean value only in the limit of large piston
mass, while they are strongly asymmetric in the opposite limit. Only taking
into account such an asymmetry, i.e. including a third parameter in addition to
the mean and the variance of the velocity distribution, it is possible to
obtain a satisfactory analytical prediction for the ratchet drift velocity.Comment: 6 pages, 5 figures, to be published on Europhysics Letters; some
references have been adde
Fluctuations in granular gases
A driven granular material, e.g. a vibrated box full of sand, is a stationary
system which may be very far from equilibrium. The standard equilibrium
statistical mechanics is therefore inadequate to describe fluctuations in such
a system. Here we present numerical and analytical results concerning energy
and injected power fluctuations. In the first part we explain how the study of
the probability density function (pdf) of the fluctuations of total energy is
related to the characterization of velocity correlations. Two different regimes
are addressed: the gas driven at the boundaries and the homogeneously driven
gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of
homogeneity in hydrodynamics profiles, even in the absence of velocity
correlations, the fluctuations of total energy are non-trivial and may lead to
erroneous conclusions about the role of correlations. In the second part of the
chapter we take into consideration the fluctuations of injected power in driven
granular gas models. Recently, real and numerical experiments have been
interpreted as evidence that the fluctuations of power injection seem to
satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an
alternative interpretation of such results which invalidates the
Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and
using techniques from large deviation theory, the general validity of a
Fluctuation Relation for power injection in driven granular gases is
questioned. Finally a functional is defined using the Lebowitz-Spohn approach
for Markov processes applied to the linear inelastic Boltzmann equation
relevant to describe the motion of a tracer particle. Such a functional results
to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure
- …