An exactly solvable toy model that mimics the mode coupling theory of supercooled liquid and glass transition

Abstract

A toy model is proposed which incorporates the reversible mode coupling mechanism responsible for ergodic-nonergodic transition with trivial Hamiltonian in the mode coupling theory (MCT) of structural glass transition. The model can be analyzed without relying on uncontrolled approximations inevitable in the current MCT. The strength of hopping processes can be easily tuned and the ideal glass transition is reproduced only in a certain range of the strength. On the basis of the analyses of our model we discuss about a sharp ergodic-nonergodic transition and its smearing out by "hopping".

5 pages, 2 ps-figures, inappropriate terms replaced

Cited by in corpus (11)

• A localization transition underlies the mode-coupling crossover of glasses
• Crossover from $\beta$- to $\alpha$-relaxation in cooperative facilitation dynamics
• Dynamic Mean-Field Glass Model with Reversible Mode Coupling and Trivial Hamiltonian
• Glass transitions and scaling laws within an alternative mode-coupling theory
• Brownian dynamics: from glassy to trivial
• Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids
• Analyses of kinetic glass transition in short-range attractive colloids based on time-convolutionless mode-coupling theory
• Kinetically driven glassy transition in an exactly solvable toy model with reversible mode coupling mechanism and trivial statics
• Scaling behavior of the self diffusion coefficients: dependence on the mass ratio of a binary mixture
• Out of equilibrium dynamics of the toy model with mode coupling and trivial Hamiltonian
• Theory of Kinetically-Constrained-Models Dynamics