Short time dynamics determine glass forming ability in a glass transition two-level model: a stochastic approach using Kramers' escape formula

Abstract

The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers transition theory, which arises in very natural manner to calculate transition rates between wells. Then the corresponding stochastic master equation is analytically solved to find the population of metastable states. A relation between the cooling rate, the characteristic relaxation time and the population of metastable states is found from the solution of such equation. From this, a relationship between the relaxation times and the frequency of oscillation at the metastable states, i.e., the short time dynamics is obtained. Since the model is able to capture either a glass transition or a crystallization depending on the cooling rate, this gives a conceptual framework in which to discuss some aspects of rigidity theory.