  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.
