Curved boundary corrections to nodal line statistics in chaotic billiards

被引:8
|
作者
Wheeler, CT [1 ]
机构
[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2005年 / 38卷 / 07期
关键词
D O I
10.1088/0305-4470/38/7/006
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A Gaussian random wavefunction that satisfies Dirichlet and Neumann conditions locally on a convex circular boundary is introduced. The average of the square of the wavefunction and its derivatives are computed and their asymptotics studied in the semi-classical limit. The mean nodal line length (L) is calculated and the first order boundary effect shown to be of order log k, where k is the wavenumber. In the limit of vanishing boundary curvature (large boundary radius) these results are shown to approach those for a straight wall boundary.
引用
收藏
页码:1491 / 1504
页数:14
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