Universal spectral form factor for chaotic dynamics

Details Universal spectral form factor for chaotic dynamics Universal spectral form factor for chaotic dynamics

2003-09-05

arxiv.org/abs/nlin/0309022v1

J. Phys. A: Math. Gen. 37, L31 (2004)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 1 figure

Scientific paper

10.1088/0305-4470/37/3/L02

We consider the semiclassical limit of the spectral form factor $K(\tau)$ of fully chaotic dynamics. Starting from the Gutzwiller type double sum over classical periodic orbits we set out to recover the universal behavior predicted by random-matrix theory, both for dynamics with and without time reversal invariance. For times smaller than half the Heisenberg time $T_H\propto \hbar^{-f+1}$, we extend the previously known $\tau$-expansion to include the cubic term. Beyond confirming random-matrix behavior of individual spectra, the virtue of that extension is that the ``diagrammatic rules'' come in sight which determine the families of orbit pairs responsible for all orders of the $\tau$-expansion.

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