Dynamics of relaxing systems subjected to nonlinear interactions

The combination of the Fermi map system and half a stadium is studied to determine the effect of additional nonlinearity in the well known Fermi acceleration problem. The relaxation in the Fermi-stadium map with different $R$’s is compared to that in the Fermi map. The relaxation is found retarded for different values of $R$. After a crossover time, the Fermi relaxation can be approximated by an exponential function, while the Fermi-stadium relaxation can be approximated by a stretched-exponential function. The fractional exponent β decreases further from unity with increasing nonlinearity. The result bears strong similarity to the basic features suggested by the coupling model and seen experimentally in glass-forming materials by neutron scattering.