New approach to periodic orbit theory of spectral correlations

DOI10.1088/1751-8121/aafadczbMath1425.81043arXiv1809.02454OpenAlexW3099075856WikidataQ128697539 ScholiaQ128697539MaRDI QIDQ5243724

Petr A. Braun, Daniel Waltner

Publication date: 19 November 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02454

zbMATH Keywords

Riemann zeta functionanalytic continuationspectral determinantsemiclassical methodsGutzwiller trace formula\(L\) --functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Quantum chaos (81Q50) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Relations with random matrices (11M50)

Cites Work

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• Chaos in classical and quantum mechanics
• The semiclassical origin of the logarithmic singularity in the symplectic form factor
• A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros
• Finite pseudo orbit expansions for spectral quantities of quantum graphs
• Beyond the Heisenberg time: semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
• Resummation and the semiclassical theory of spectral statistics
• Then-level spectral correlations for chaotic systems
• The Riemann Zeros and Eigenvalue Asymptotics
• Semiclassical theory of spectral rigidity
• Random matrix theory and the Riemann zeros II:n-point correlations
• Spectral statistics for the Dirac operator on graphs
• Correlations in the actions of periodic orbits derived from quantum chaos
• Semiclassical form factor for chaotic systems with spin ½
• The semiclassical functional equation
• The Riemann-Siegel expansion for the zeta function: high orders and remainders
• Random matrix theory and the Riemann zeros. I. Three- and four-point correlations
• Two-point correlation function for DirichletL-functions
• Applications of theL-functions ratios conjectures
• Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Riemann Zeta Function and Quantum Chaos
• Quantum signatures of chaos

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