PERIODIC LIBRATIONS AND THEIR EFFECT ON THE QUANTUM ENERGY-SPECTRUM

被引:9
作者
DEALMEIDA, AMO
DEAGUIAR, MAM
机构
[1] MIT, CTR THEORET SCI, NUCL SCI LAB, CAMBRIDGE, MA 02139 USA
[2] MIT, DEPT PHYS, CAMBRIDGE, MA 02139 USA
关键词
D O I
10.1016/0167-2789(90)90006-B
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:391 / 402
页数:12
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