Quantum and Arithmetical Chaos

Abstract

The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and of the Laplace--Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical methods of quantum chaos.

Lectures given at Les Houches School "Frontiers in Number Theory, Physics and Geometry" March 2003

References in corpus (4)

• Spectral Statistics Beyond Random Matrix Theory
• Distribution of Eigenvalues for the Modular Group
• The correlation between multiplicities of closed geodesics on the modular surface
• Spectral statistics and periodic orbits

Cited by in corpus (3)

• On the spacing distribution of the Riemann zeros: corrections to the asymptotic result
• Riemann zeta function and quantum chaos
• The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime