Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2004-01-15
Phys.Rev.Lett. 93 (2004) 014103
Nonlinear Sciences
Chaotic Dynamics
4 pages, 2 figures; final version published in PRL, minor changes
Scientific paper
10.1103/PhysRevLett.93.014103
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the non-linear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.
Altland Alexander
Braun Petr
Haake Fritz
Heusler Stefan
Müller Sebastian
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