Andre L. P. Livorati, Tiago Kroetz, Carl P. Dettmann, Ibere Luiz Caldas, Edson D. Leonel. Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
Natural Sciences / Physics / Mathematical Physics
Submitted on: Sep 13, 2012, 16:44:19
Description: Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is characterized by a control parameter $epsilon$ and experiences a transition from integrable ($epsilon=0$) to non integrable ($epsilonne 0$). For small values of $epsilon$, the phase space shows a mixed structure where periodic islands, chaotic seas and invariant tori coexist. As the parameter $epsilon$ increases and reaches a critical value $epsilon_c$ all invariant tori are destroyed and the chaotic sea spreads over the phase space leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space.