Non-Arrhenius relaxation effects in collections of two-level subsystems

摘要

We present numerical simulations of relaxation isotherms for an ensemble of thermally activated, two-level subsystems, with double-well free energy profiles, and with a distribution of dissipation barriers and level splittings. The field history imitates a typical experimental viscosity protocol, and consists of saturation in a large positive field, followed by recoil to a negative holding field, and then by the thermally driven decay of the moment towards equilibrium at fixed temperature and fixed field. The numerical simulations show that systems whose relaxation dynamics are governed explicitly by the Arrhenius law of thermal activation, can exhibit relaxation effects which are apparently "non-Arrhenius" in origin. In particular, the maximum value of the relaxation rate S ≡ -(partial deriv)M(t)/(partial deriv)ln t extracted from model viscosity isotherms over a typical experimental time window 100 s ≤ t ≤10~4 s, and the thermal viscosity field H_f(T) extracted, over the same time window, from the field dependence of the logarithm of the time at which the moment reverses direction as it relaxes towards equilibrium, both exhibit variations with temperature which are highly nonlinear, and which are characterized by coincident maxima, very similar to those observed experimentally in a variety of particulate systems.