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Article

Narrow- tube approximation of semiclassical quasi energies: - application to the weakly non-linear Duffing oscillators.

Authors: Thylwe, K.-E., Bensch, F.
Document Type: Article
Pubstate: Published
Journal: J. Phys. A: Math. Gen.
Volume: 27   5673-5684
Year: 1994

Abstract

An exact transformation of semiclassical quantization conditions determining quantal quasi-energies of time-periodic Hamiltonian systems is suggested. For motion on vortex tubes centred at stable periodic orbits the classical quasi-energy of the underlying periodic orbit separates out as a single term which is a lower bound for the quantized quasi-energies. A particular approximation involving the classical Lewis invariant for calculating semiclassical quasi-energies near the centre of a perturbed linear response is discussed in some detail.