Classical resonances and an arbitrary trajectory quantization scheme for a chaotic system

Abstract

The exponential decay of correlations in chaotic systems is often modulated and shows up as broad peaks in the power spectrum. For a particle sliding freely on a compact surface of constant negative curvature, we show that these classical resonances are directly related to the quantal eigenenergies of the system. We use this as the basis for proposing a quantization scheme which requires the knowledge of a single arbitrary ergodic classical trajectory. Our results are substantiated numerically.