AVALANCHE PHENOMENA IN TWO-DIMENSIONAL FOAM SYSTEMS(Session III : Complex Fluids, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

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A FDR-preserving field theory for interacting Brownian particles: one-loop theory and MCT

We develop a field theoretical treatment of a model of interacting Brownian particles. We pay particular attention to the requirement of the time reversal invariance and the fluctuation-dissipation relationship (FDR). The method used is a modified version of the auxiliary field method due originally to Andreanov, Biroli and Lefevre [J. Stat. Mech. P07008 (2006)]. We recover the correct diffusion law when the interaction is dropped as well as the standard mode coupling equation in the one-loop order calculation for interacting Brownian particle systems.Comment: 66 pages, 8 figures, submitted to J. Stat. Mec

Mode coupling theory in the FDR-preserving field theory of interacting Brownian particles

We develop a renormalized perturbation theory for the dynamics of interacting Brownian particles, which preserves the fluctuation-dissipation relation order by order. We then show that the resulting one-loop theory gives a closed equation for the density correlation function, which is identical with that in the standard mode coupling theory.Comment: version to be published in Fast Track Communication in Journal of Physics A:Math. Theo

Kinetically driven glassy transition in an exactly solvable toy model with reversible mode coupling mechanism and trivial statics

We propose a toy model with reversible mode coupling mechanism and with trivial Hamiltonian (and hence trivial statics). The model can be analyzed exactly without relying upon uncontrolled approximation such as the factorization approximation employed in the current MCT. We show that the model exhibits a kinetically driven transition from an ergodic phase to nonergodic phase. The nonergodic state is the nonequilibrium stationary solution of the Fokker-Planck equation for the distribution function of the modelComment: 10 pages, 1 figure, contribution to the Proceedings of the Barcelona Workshop 'Glassy Behavior of Kinetically Constrained Models'. To appear in J. Phys. Condens. Matte

Dynamic Mean-Field Glass Model with Reversible Mode Coupling and Trivial Hamiltonian

Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise account of our toy model developed to gain more insight into MCT. We then reduce this toy model by adiabatically eliminating rapidly varying velocity-like variables to obtain a Fokker-Planck equation for the slowly varying density-like variables where diffusion matrix can be singular. This gives a room for nonergodic stationary solutions of the above equation.Comment: 9 pages, contribution to the Proceedings of the Merida Satellite Meeting to STATPHYS21 (Merida, Mexico, July 9-14, 2001). To appear in J. Phys. Condens. Matte