Spectrum sensitivity in a chaotic quantum system

The sensitive dependence of the positions of the discrete spectrum energy l evels E-n on the parameter alpha of the Hamiltonian is studied, using the e xample of a nonlinear perturbed quantum oscillator with two degrees of free dom (the Henon-Heiles model), which in the classical case exhibits stochast ic dynamics. It is shown that large susceptibilities chi (alpha)(n)=d(2)En( alpha)/d alpha (2) may occur both in regions of the parameter where the mot ion of the system is close to regular motion, and in regions where it is cl ose to ergodic motion. Analytic estimates are obtained for the values of ch i (alpha) in these regions, estimates which agree with the results of compu ter experiments. (C) 2001 Elsevier Science Ltd. All rights reserved.