A rule for quantizing chaos?

Abstract

The authors find a real function Delta (E) whose zeros approximate the quantum energy levels of a system with chaotic classical trajectories. Delta (E) is a finite sum over combinations of classical periodic orbits. It is obtained from Gutzwiller's infinite and divergent sum (1982), representing the spectral density in terms of periodic orbits, by means of a resummation conjectured by analogy with a derivation of the Riemann-Siegel formula for the Riemann zeros. They assess the practicality of the quantization condition.