Localization in Infinite Billiards: A Comparison Between Quantum and Classical Ergodicity

被引：0

作者：

Sandro Graffi

Marco Lenci

机构：

[1] Università di Bologna,Dipartimento di Matematica

[2] Stevens Institute of Technology,Department of Mathematical Sciences

来源：

Journal of Statistical Physics | 2004年 / 116卷

关键词：

ergodicity; quantum ergodicity; quantum chaos; localization; non-compact billiards; cusps;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Consider the non-compact billiard in the first quandrant bounded by the positive x-semiaxis, the positive y-semiaxis and the graph of f(x)=(x+1)−α, α∈(1,2]. Although the Schnirelman Theorem holds, the quantum average of the position xis finite on any eigenstate, while classical ergodicity entails that the classical time average of xis unbounded.

引用

页码：821 / 830

页数：9

共 34 条

[1]

Bourgain J.(2003)Entropy of quantum limits Comm. Math. Phys. 233 153-171

[2]

Lindenstrauss E.(1985)Ergodicité et fonctions propres du laplacien Comm. Math. Phys. 102 497-502

[3]

Colin de Verdière Y.(1985)Trace properties of the Dirichlet Laplacian Math. Zeit. 188 245-251

[4]

Davies E. B.(1992)Spectral properties of the Neumann Laplacian of horns Geom. Funct. Anal. 2 105-117

[5]

Davies E. B.(1995)Stochastic properties of the quantum toral automorphisms at the classical limit Comm. Math. Phys. 167 471-507

[6]

Simon B.(1987)Ergodicité et limite semi-classique Comm. Math. Phys. 109 313-326

[7]

Degli Esposti M.(1996)Escape orbits for non-compact flat billiards Chaos 6 428-431

[8]

Graffi S.(2002)Semidispersing billiards with an infinite cusp. I Comm. Math. Phys. 230 133-180

[9]

Isola S.(2003)Semidispersing billiards with an infinite cusp. II Chaos 13 105-111

[10]

Helffer B.(2001)On quantum unique ergodicity for г\ℍх ℍ Internat. Math. Res. Notices 17 913-933

← 1 2 3 4 →