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Type: Artigo de periódico
Title: Periodic Librations And Their Effect On The Quantum Energy Spectrum
Author: De Almeida A.M.O.
De Aguiar M.A.M.
Abstract: Classical Hamiltonian systems with time-reversal symmetry have periodic orbits of two kinds-symmetry pairs (rotations) and self-symmetric orbits (librations). For integrable anharmonic oscillators with two freedoms, almost all of periodic orbits of any period are rotation pairs. However, we show that a KAM-type perturbation alters this balance, such that a finite fraction of the low-period orbits are librations. The generic bifurcations undergone by librations are isomorphic to those of non-symmetric orbits of structurally stable Hamiltonians, with the addition of an extra type of periodic bifurcation. We determine the unfolding of this bifurcation as time-reversal symmetry is broken. The effect of this non-structurally stable bifurcation on the quantum mechanical density of states is also obtained. The present results also hold for systems that are symmetric with respect to general anti-unitary symmetries in quantum mechanics, corresponding to anticanonically reversible Hamiltonian classical systems. © 1990.
Rights: fechado
Identifier DOI: 10.1016/0167-2789(90)90006-B
Date Issue: 1990
Appears in Collections:Unicamp - Artigos e Outros Documentos

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