Monday 07 Oct 2013Fermi acceleration in time-dependent billiards

Dimitry Turaev - Imperial college

Harrison 101 15:00-16:00

We discuss a novel theory of the evolution of energy in billiards with slowly moving boundaries. The theory
is based on the Anosov-Kasuga theory of adiabatic invariants. We propose a stochastic description for the energy evolution, and demonstrate that the ergodicity of the billiard impedes the energy transfer from the moving boundary to the particle inside the billiard. We describe recent examples of time-dependent billiards for which a controlled violation of ergodicity leads to an exponential energy growth, i.e. to the energy transfer which is much more effective than in the ergodic case. We argue that the effect is of a fairly general nature: For slow-fast Hamiltonian systems with chaotic behaviour in the fast variables, the periodic violation of ergodicity must be the key mechanism behind a sustained energy flow from slow to fast degrees of freedom and an anomalous statistics of high-energy orbits.

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