SEMICLASSICAL TRACE FORMULAS IN THE PRESENCE OF CONTINUOUS SYMMETRIES

被引:102
作者
CREAGH, SC [1 ]
LITTLEJOHN, RG [1 ]
机构
[1] UNIV CALIF BERKELEY, BERKELEY, CA 94720 USA
来源
PHYSICAL REVIEW A | 1991年 / 44卷 / 02期
关键词
D O I
10.1103/PhysRevA.44.836
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We derive generalizations of the semiclassical trace formula of Gutzwiller [J. Math. Phys. 12, 343 (1971)] and Balian and Bloch [Ann. Phys. 69, 76 (1972)] that are valid for systems exhibiting continuous symmetries. In particular, we consider symmetries for which the associated set of conserved quantities Poisson-commute. For these systems, the periodic orbits of a given energy occur in continuous families and the usual trace formula, which is valid only when the periodic orbits of a given energy are isolated, does not apply. In the trace formulas we derive, the density of states is determined by a sum over continuous families of periodic orbits rather than a sum over individual periodic orbits. Like Gutzwiller's formula for isolated orbits, the sum involves intrinsic, canonically invariant properties of the periodic orbits. We illustrate the theory with two important special cases: axial symmetry and integrable systems.
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页码:836 / 850
页数:15
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