CLASSICAL RESONANCES AND AN ARBITRARY TRAJECTORY QUANTIZATION SCHEME FOR A CHAOTIC SYSTEM

The exponential decay of correlations in chaotic systems is often modu lated and shows up as broad peaks in the power spectrum. For a particl e sliding freely on a compact surface of constant negative curvature, we show that these classical resonances are directly related to the qu antal eigenenergies of the system. We use this as the basis for propos ing a quantization scheme which requires the knowledge of a single arb itrary ergodic classical trajectory. Our results are substantiated num erically.