Coarse-grained forms for equations describing the microscopic motion of particles in a fluid

Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory. In the thermally averaged equation for the coarse grained density ${\rho}({\bf x},t)$, the related dependence on the bare interaction potential in Dean's equation is converted to that on the corresponding direct correlation functions of the density functional theory.Comment: 10 page

Temperature dependence of the Power law exponent of relaxation in a supercooled Liquid

The dynamics of Lennard-Jones fluid is studied through extended mode coupling theory (MCT) with the inclusion of the slow mode of defect density. Inclusion of defect density facilitates the liquid like state for temperatures much lower than predicted from ideal MCT. From the present model the temperature dependence of the power law exponent is obtained at a {\em constant pressure}. We have also computed the wave number dependence of the power law exponent.Comment: 10 pages, 6 figure

Transport coefficients at Metastable Densities from models of Generalized Hydrodynamics

In the present work we compute the enhancement in the long time transport coefficients due to correlated motion of fluid particles at high density. The fully wave vecor dependent extended mode coupling model is studied with the inclusion of an additional slow variable of the defect density for the amorphous system. We use the extremely slow relaxation of the density correlation function observed in the light scattering experiments on colloids to estimate the input parameters for the model The ratio of long time to short time diffusion coefficient is studied around the the peak of the structure factor.Comment: 17 pages, 8 figure

Fragility and Boson Peak formation in a Supercooled Liquid

We analyze results for the Boson Peak from the neutron time of flight spectroscopy data on Ge-As-Se, and Raman spectra data on m-TCP and OTP, using a recent mode coupling model that takes into account the coupling of density fluctuations with vibrational modes in presence of defects in the supercooled state. From the experimental results for different materials we observe that for more fragile systems characterized by increasing fragility parameter m, a slower relaxation of the defect-density correlation is needed to give rise to the observed peak in the spectra.Comment: 6 pages, 5 figure

Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables $\rho$, the number density, and $B$, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.Comment: 48 pages, 3 figure

Glassy Aging with Modified Kohlrausch-Williams-Watts Form

In this report we address the question whether aging in the non equilibrium glassy state is controlled by the equilibrium alpha-relaxation process which occur at temperatures above Tg. Recently Lunkenheimer et. al. [Phys. Rev. Lett. 95, 055702 (2005)] proposed a model for the glassy aging data of dielectric relaxation using a modified Kohlrausch-Williams-Watts (KWW) form. The aging time dependence of the relaxation time is defined by these authors through a functional relation involving the corresponding frequency but the stretching exponent is same as the alpha-relaxation stretching exponent. We present here an alternative functional form directly involving the relaxation time itself. The proposed model fits the data of Lunkenheimer et. al. perfectly with a stretching exponent different from the alpha-relaxation stretching exponent.Comment: 1 TeX file, 10 eps figure

Field Theoretic Formulation of Kinetic theory: I. Basic Development

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables \rho the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables \rho and B.Comment: 45 page