Properties of vibrational energy levels in the quasi periodic and stochastic regimes

Abstract

Several aspects of the quantal energy spectrum are explored for the Henon–Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the quasiperiodic to the stochastic regime, the origin of large second differences Δ2Ei of eigenvalues arising from variation of a parameter, the comparison of classical and quantal spectra, and a comparison of the ’’classical’’ and quantal number of states. In the study of the second differences we find both ’’crossings’’ and ’’avoided crossings’’ of the eigenvalues. We discuss the importance of overlapping avoided crossings as a basis for a possible theory of ’’quantum stochasticity’’.