Fermi acceleration and its suppression in a time-dependent Lorentz gas |
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Authors: | Diego F.M. Oliveira Jürgen Vollmer Edson D. Leonel |
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Affiliation: | 1. Max Planck Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073, Göttingen, Germany;2. CAMTP—Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia;3. Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Av. 24A, 1515, Bela Vista, CEP: 13506-900, Rio Claro, SP, Brazil |
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Abstract: | Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. |
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