Waiting time dependence of aging.

Aging phenomena have been observed in many non-equilibrium systems such as polymers and glasses, where physical properties depend on the waiting time between the starting time of observation and the time when the temperature is changed. The aging is classified into two types on the basis of the waiting time dependence of an instantaneous relaxation time: When the relaxation time is always an increasing function of the waiting time, the aging is called Type I and when it depends on the protocol of the temperature change, the aging is called Type II. Aging of a random walk in three dimensions is investigated when the free energy landscape controlling the jump rate responds to temperature change with a delay. It is shown that the intermediate scattering function of the random walk model exhibits Type II aging. It is also shown that the relaxation time of the free energy landscape can be deduced from the waiting time dependence of the instantaneous relaxation time.