2019/10/31 by Roman Riser, Vladimir Al. Osipov, Eugene Kanzieper · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.dis-nn #hep-th #math.MP #nlin.CD #quant-ph
paper · pdf · doi:10.1016/j.aop.2019.168065
published as Annals of Physics 413, 168065 (2020) · 48 pages, 5 fugures; published version (typos corrected)
arxiv created 2020/01/22 · arxiv updated 2020/01/23
The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for complex systems whose eigenspectra -- not necessarily of the random-matrix-theory (RMT) type -- posses stationary level spacings. Motivated by potential applications in quantum chaology, we apply our formalism to calculate the power spectrum in a tuned circular ensemble of random N × N unitary matrices. In the limit of infinite-dimensional matrices, the exact solution produces a universal, parameter-free formula for the power spectrum, expressed in terms of a fifth Painlevé transcendent. The prediction is expected to hold universally, at not too low frequencies, for a variety of quantum systems with completely chaotic classical dynamics and broken time-reversal symmetry. On the mathematical side, our study brings forward a conjecture for a double integral identity involving a fifth Painlevé transcendent.