Spectrum sensitivity in a chaotic quantum system

The sensitive dependence of the positions of the discrete spectrum energy levels En on the parameter α of the Hamiltonian is studied, using the example of a nonlinear perturbed quantum oscillator with two degrees of freedom (the Hénon–Heiles model), which in the classical case exhibits stochastic dynamics. It is shown that large susceptibilities may occur both in regions of the parameter where the motion of the system is close to regular motion, and in regions where it is close to ergodic motion. Analytic estimates are obtained for the values of χα in these regions, estimates which agree with the results of computer experiments.