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

Abstract

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.

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. Matter

References in corpus (1)

• Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids

Cited by in corpus (7)

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• Brownian dynamics: from glassy to trivial
• Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids
• Theory of Kinetically-Constrained-Models Dynamics
• Out of equilibrium dynamics of the toy model with mode coupling and trivial Hamiltonian