Phase-integral quantization of accidentally and intrinsically degenerate nonlinear systems

Abstract

The dynamics of many nonlinearly coupled oscillator systems with internal resonances resembles the motion of a pendulum. For some other resonant systems the dynamics in the vicinity of the resonance cannot be mapped onto this “Standard Hamiltonian” of nonlinear theory. Often these two varieties, called “accidentally” and “intrinsically” degenerate systems respectively, can be converted into each other by changing external parameters. In this article, we introduce an alternative mapping (to the “Standard Map”) valid for both kinds of degeneracies by exploiting a connection between oscillator systems and asymmetric rotors. We apply this mapping to the phase-integral quantization to degenerate oscillator systems.