Periodic Orbits and Semiclassical Form Factor in Barrier Billiards

被引：0
作者：
O. Giraud
机构：
[1] Université Paul Sabatier,Laboratoire de Physique théorique, UMR 5152 du CNRS
来源：
Communications in Mathematical Physics | 2005年 / 260卷
关键词：
Neural Network; Statistical Physic; Complex System; Periodic Orbit; Nonlinear Dynamics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orbits by a Siegel-Veech formula. The result [inline-graphic not available: see fulltext] obtained for these pseudo-integrable, non-Veech billiards is different but not far from the value of 1/2 expected for semi-Poisson statistics and from values of [inline-graphic not available: see fulltext] obtained previously in the case of Veech billiards.
引用
收藏
页码：183 / 201
页数：18
相关论文
共 28 条
  • [1] Agam O.(1995)Intermediate statistics in quantum maps Phys. Rev. Lett 75 4389-L311
  • [2] Andreev J.(1995)undefined Phys. Rev. Lett. 75 902-undefined
  • [3] Balian S.(1972)undefined Ann. Phys. (N.Y.) 69 76-undefined
  • [4] Berry undefined(1985)undefined Proc. Roy. Soc. A 400 229-undefined
  • [5] Richens undefined(1981)undefined Physica D 2 495-undefined
  • [6] Berry undefined(1976)undefined Proc. Roy. Soc. Lond. A 349 101-undefined
  • [7] Berry undefined(1977)undefined Proc. Roy. Soc. Lond. A 356 375-undefined
  • [8] Bohigas undefined(1984)undefined Phys. Rev. Lett. 52 1-undefined
  • [9] Bogomolny undefined(2000)undefined Nonlinearity 13 947-undefined
  • [10] Bogomolny undefined(2000)undefined Phys. Rev. E 61 3689-undefined
123