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arXiv · 1206.4222

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

P. Braun·F. Haake
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Abstract

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike.

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P. Braun, F. Haake. 2012-06-19. Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations. https://doi.org/10.1088/1751-8113/45/42/425101

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