Isaac Newton Institute for Mathematical Sciences

Bunched periodic orbits: The skeleton of classical and quantum chaos

Authors: Alexander Altland (Universität zu Köln, Germany), Petr Braun (Universität Duisburg-Essen, Germany), Fritz Haake (Universität Duisburg-Essen, Germany), Stefan Heusler (Westfälische Wilhelms-Universität Münster, Germany), Gerhard Knieper (Ruhr-Universität Bochum, Germany), Sebastian Müller (University of Bristol, UK)

Abstract

It was recently discovered that long (quasi-ergodic) orbits of chaotic dynamics come in closely packed bunches. Under weak resolution a bunch looks like a single orbit but in fact the orbits are topologically distinct. The construction principle of bunches is related to close self-encounters wherein two or more stretches of one orbit lie very close.

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.