Resummation and the semiclassical theory of spectral statistics

Abstract

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.

10 pages, no figures

References in corpus (4)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Universal spectral correlations from the ballistic sigma model

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• Periodic-orbit theory of universal level correlations in quantum chaos
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Semiclassical roots of universality in many-body quantum chaos
• Semiclassical approach to discrete symmetries in quantum chaos
• Anderson localization from classical trajectories
• Some open questions in "wave chaos"
• Universality of Level Spacing Distributions in Classical Chaos
• Quantum chaos in one dimension?
• Semiclassical spectral correlator in quasi one-dimensional systems