Effects of bifurcations on the energy level statistics for oval billiards
Effects of bifurcations on the energy level statistics for oval billiards
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分岔对椭圆台球能级统计的影响
DOI：
10.1103/physreve.59.4026
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Y. Aizawa
中科院分区：
文献类型：
--
作者：
H. Makino;T. Harayama;Y. Aizawa
我们研究了椭圆台球的一个参数族的能级统计，其经典相空间由一些规则分量和一些不规则分量组成。随着参数的变化，从可积系统到强混沌系统的转变会随着连续的分叉而发生。我们将 Berry-Robnik 公式应用于各种形状的量子椭圆台球的能级间距分布，并发现经典机械系统中的分岔对能级间距分布的一些显着影响。对于相空间中存在两个分离的混沌分量的椭圆台球形状，还检查了 Berry-Robnik 公式的有效性。
We studied the energy level statistics for one parameter family of oval billiards whose classical phase space consists of some regular and some irregular components. As the parameter is varied, a transition from an integrable system to a strongly chaotic one occurs with successive bifurcations. We applied the Berry-Robnik formula to the level-spacing distributions for a variety of shapes of quantum oval billiards and found some striking effects of bifurcations in the classical mechanical systems on the level-spacing distributions. The validity of the Berry-Robnik formula is also checked for those shapes of the oval billiard for which there exist two separated chaotic components in the phase space.