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

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.

References in corpus (6)

• Periodic-Orbit Theory of Level Correlations
• Periodic-orbit theory of universal level correlations in quantum chaos
• Resummation and the semiclassical theory of spectral statistics
• Finite pseudo orbit expansions for spectral quantities of quantum graphs
• Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
• Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

Cited by in corpus (4)

• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Late time physics of holographic quantum chaos
• Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
• A sub-determinant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs