Phase-integral quantization of accidentally and intrinsically degenerate nonlinear systems
type: Item
instance of: scholarly article
title: Phase-integral quantization of accidentally and intrinsically degenerate nonlinear systems
zbMATH Open document ID: 0706.58019
DOI: 10.1016/0167-2789(89)90247-9
author: T. Uzer
published in: Physica D
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 4159674
zbMATH Keywords: nonlinear oscillators
zbMATH Keywords: coupled oscillator systems
zbMATH Keywords: asymmetric rotors
zbMATH Keywords: phase-integral quantization
reviewed by: Ubiratan D'Ambrosio
MaRDI profile type: Publication
full work available at URL: 0167-2789(89)90247-9
OpenAlex ID: W2082290810
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description: scientific article; zbMATH DE number 4159674