CHAOTIC SPECTRA OF CLASSICALLY INTEGRABLE SYSTEMS

We prove that any spectral sequence obeying a certain growth law is the quantum spectrum of an equivalence class of classically integrable nonlinear oscillators. This implies that exceptions to the Berry-Tabor rule for the distribution of quantum energy gaps of classically integrable systems, are far more numerous than previously believed. in particular, we show that for each finite dimension k, there are an infinite number of classically integrable k-dimensional nonlinear oscillators whose quantum spectrum reproduces the imaginary part of zeros on the critical line of the Riemann zeta function.