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 beta 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.