The Quantum Double Pendulum: a Study of an Autonomous Classically Chaotic Quantum System

A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter containing Planck’s constant. Comparison with classical and semiclassical results is used to understand the behaviour of the energy curves of the levels, to define regimes in terms of the gravity parameter, and to classify the (resonant) interactions among levels by connecting them to various classical phase space structures (resonance islands).