Level spacings and periodic orbits

Abstract

Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this representation for the nearest-neighbor level spacing (k=0). In a second part, we present an asymptotic evaluation for large spacings, where consistency with random matrix theory is achieved for large k. We also discuss the relation with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for two-point correlations.

4 pages, 2 figures; major revisions in the second part, range of validity of asymptotic evaluation clarified

References in corpus (4)

• A semiclassical approach to the Dirac equation
• Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
• Semiclassical form factor for chaotic systems with spin 1/2
• Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

Cited by in corpus (1)

• The Wigner distribution and 2D classical maps