Semiclassical initial value approach for chaotic long-lived dynamics

A time-dependent initial value semiclassical propagator approach is developed and applied to the propagation of a two-dimensional quantum system whose classical counterpart is highly chaotic. The energy spectrum of a quartic oscillator, obtained from the propagated wavefunction, is shown to be accurately and simply computed by application of stationary-phase Monte Carlo integration. Chaotic trajectories are handled naturally, without giving rise to the singularities seen in other methods.