Semiclassical wavefunction in the chaotic region from a quantizing cantorus

Abstract

In a test system of two kinetically coupled Morse oscillators, we develop a method to construct a semiclassical wave function in the chaotic region of phase space for a cantorus satisfying EBK-like quantization conditions. The phase factor is generated by evolving classical trajectories of points on the manifolds of the quantizing cantorus. Good phase coherence is obtained when the cantorus satisfies the quantization conditions. The amplitude factor is obtained by counting the number of visits to a given spatial cell, from many trajectories distributed widely inside the chaotic sea. The resulting semiclassical wave function agrees well with the quantum wave function, comparable to semiclassical wave functions calculated from invariant EBK tori in the regular region.