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Characteristic times for the Fermi-Ulam Model

The mean Poincarré recurrence time as well as the Lyapunov time are measured for the Fermi-Ulam model. We confirm the mean recurrence time is dependent on the size of the window chosen in the phase space to where particles are allowed to recur. The fractal dimension of the region is determined by the slope of the recurrence time against the size of the window and two numerical values were measured: (i) $μ$ = 1 confirming normal diffusion for chaotic regions far from periodic domains and; (ii) $μ$ = 2 leading to anomalous diffusion measured near periodic regions, a signature of local trapping of an ensemble of particles. The Lyapunov time is measured over different domains in the phase space through a direct determination of the Lyapunov exponent, indeed being defined as its inverse.