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Accueil du site > Séminaires > Séminaires 2007 > Bunched periodic orbits : The skeleton of classical and quantum chaos

Mardi 29/05/2007 - 14H00

Bunched periodic orbits : The skeleton of classical and quantum chaos

Fritz Haake

par Didier Poilblanc - 29 mai 2007

It was recently discovered that long (quasi-ergodic) periodic orbits of fully chaotic dynamics come in narrowly packed bunches. Under weak resolution a bunch looks like a single orbit but in fact the orbits contained are topologically distinct. The construction principle of bunches is related to close self-encounters of long orbits wherein two or more stretches of one orbit lie very close. The various stretches within such an encounter can be switched so as to differently connect the orbit pieces linking the encounters. Each such reconnection leads to a different orbit but all the orbits so generated look nearly the same outside the encounters.

In particular, for close enough self-encounters the orbits in a bunch have arbitrarily small action differences and therefore give rise to constructively interfering quantum amplitudes. That latter constructive interference turns out to be the basis of universal fluctuations in quantum energy spectra and conduction properties of chaotic dynamics.