A dynamic mean-field glass model with reversible modecoupling and a trivial Hamiltonian

Abstract

Often the current mode coupling theory (MCT) of glass transitionsis compared with mean field theories. We explore this possiblecorrespondence. After showing a simple-minded derivation of MCTwith some difficulties we give a concise account of our toymodel developed to gain more insight into MCT. We then reducethis toy model by adiabatically eliminating rapidly varyingvelocity-like variables to obtain a Fokker-Planck equation forthe slowly varying density-like variables where the diffusion matrixcan be singular. This gives room for non-ergodicstationary solutions of the above equation.