Periodic orbits and trace formula - Integrable systems

The two-dimensional uncoupled quartic oscillator was chosen to test the val idity of the Berry-Tabor trace formula. Periodic orbits of the system were calculated by integrating Hamiltonian equations of motion on reasonable tor i and the curvatures on the energy surface were obtained by carefully const ructing the orbits around the reasonable tori. Finally, the value of the se miclassical action function and that of the quantum action function in the case S < 30 were compared, and the good agreement between the two functions indicates the validity of the trace formula. On the other hand, in the qua ntum action function R-QM ( S, E ) - S figuration, that peaks appeared at t he action values corresponding to the periodic orbits of the classical syst em provide rich information on quantum-classical correspondence.