Phase-integral quantization of accidentally and intrinsically degenerate nonlinear systems
Consider coupled nonlinear systems. Degeneracies, in the sense of existence of nonlinear resonance, occur in these systems both as accidentally and intrinsically. It is known that accidentally degenerate two-degree of freedom Hamiltonians can be transformed to a pendulum Hamiltonian called ``standard Hamiltonian'', whereas in general an intrinsically degenerate Hamiltonian can merely be mapped onto a harmonic oscillator. This paper introduces a new mapping alternative for the two degeneracies. This is done by exploiting a connection between oscillator systems and asymmetric rotors. Then the author applies this mapping to derive a phase-integral quantization scheme valid for both accidental and intrinsic degeneracies.
scientific article; zbMATH DE number 4159674
scientific article