R Egydio de Carvalho et al 2006 J. Phys. A: Math. Gen. 39 3561 doi:10.1088/0305-4470/39/14/005
Fermi acceleration on the annular billiard: a simplified version
R Egydio de Carvalho, F Caetano de Souza and Edson D Leonel
Show affiliationsA simplified version of a time-dependent annular billiard is studied. The dynamics is described using nonlinear maps and we consider two different configurations for the billiard, namely (i) concentric and (ii) eccentric cases. For the concentric case and for a null angular momentum, we confirm that the results for the Fermi–Ulam model are recovered and the particle does not experience the phenomenon of Fermi acceleration. However, on the eccentric case the particle demonstrates unlimited energy gain and Fermi acceleration is therefore observed.
- PACS
- MSC
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37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (See also 53D20)
37A25 Ergodicity, mixing, rates of mixing
37D50 Hyperbolic systems with singularities (billiards, etc.)
- Subjects
- Dates
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Issue 14 (7 April 2006)
Received 8 November 2005, in final form 26 January 2006
Published 22 March 2006
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Fermi acceleration on the annular billiard: a simplified version
R Egydio de Carvalho et al 2006 J. Phys. A: Math. Gen. 39 3561
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