Resummation and the semiclassical theory of spectral statistics

Details Resummation and the semiclassical theory of spectral statistics Resummation and the semiclassical theory of spectral statistics

2007-08-17

arxiv.org/abs/0708.2375v1

Proc. R. Soc. Lond. A 463, 3241 (2007)

Nonlinear Sciences

Chaotic Dynamics

10 pages, no figures

Scientific paper

10.1098/rspa.2007.0178

We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation formalism that explicitly preserves the unitarity of the quantum time evolution by incorporating duality relations between short and long classical orbits. This allows us to obtain both the non-oscillatory and the oscillatory contributions to spectral correlation functions within a unified framework, thus overcoming a significant problem in previous approaches. In addition, our results extend beyond the universal regime to describe the system-specific approach to the semiclassical limit.

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