Resummation and the semiclassical theory of spectral statistics

Jon P Keating, Sebastian Muller

Research output: Contribution to journalArticle (Academic Journal)peer-review

29 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)3241-3250
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publication statusPublished - 2007

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