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 $N$-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 $N$-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