Exponential energy growth in a Fermi accelerator

Kushal Shah, Dmitry Turaev, Vered Rom-Kedar

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


An unbounded energy growth of particles bouncing off two-dimensional (2D) smoothly oscillating polygons is observed. Notably, such billiards have zero Lyapunov exponents in the static case. For a special 2D polygon geometry-a rectangle with a vertically oscillating horizontal bar-we show that this energy growth is not only unbounded but also exponential in time. For the energy averaged over an ensemble of initial conditions, we derive an a priori expression for the rate of the exponential growth as a function of the geometry and the ensemble type. We demonstrate numerically that the ensemble averaged energy indeed grows exponentially, at a close to the analytically predicted rate-namely, the process is controllable.

Original languageEnglish
Article number056205
JournalPhysical Review E
Issue number5
StatePublished - 17 May 2010
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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