Deformations and dilations of chaotic billiards: Dissipation rate, and quasiorthogonality of the boundary wave functions

被引：26

作者：

Barnett, A ^{[1
]}

Cohen, D ^{[1
]}

Heller, EJ ^{[1
]}

机构：

[1] Harvard Univ, Dept Phys, Cambridge, MA 02138 USA

来源：

PHYSICAL REVIEW LETTERS | 2000年 / 85卷 / 07期

关键词：

Boundary wave functions - Chaotic billiards - Dilations - Eigenstates - Generic deformation - Matrix elements - Quasiorthogonality;

D O I：

10.1103/PhysRevLett.85.1412

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider chaotic billiards in d dimensions, and study the matrix elements M-nm corresponding to general deformations of the boundary. We analyze the dependence of \Mnm\(2) on omega = (E-n - E-m)/h using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency w. We show that, for dilations and translations of the boundary, \M-nm\(2) vanishes like omega(4) as omega --> 0, for rotations such as omega(2), whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.

引用

页码：1412 / 1415

页数：4

共 16 条

[1] DIABOLICAL POINTS IN THE SPECTRA OF TRIANGLES [J].