|Other titles||Two-point spectral correlations for the square billiard.|
|Statement||J.P. Keating, R.D. Connors.|
|Series||[Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-29., BRIMS technical report -- HPL-BRIMS-96-29.|
|Contributions||Connors, R. D., Hewlett-Packard Laboratories.|
|The Physical Object|
|Pagination||21 p. :|
|Number of Pages||21|
The square billiard, though completely integrable, is non-genericin this respect. Its levels, when suitably scaled, are given by E 2 2 m,n = m +n (m, n) E If,(m, n) =I (0,0), (1) and so the density of states may be written in the form 00 d(E) =L r2(n) 6(E - n). n=l (2) where r2 (n) is the number of ways that n can be written as a sum of two squares. 2-point spectral correlations for the square billiard. By J. Keating, R. Connors and Bristol (United Kingdom) 12A - Pure mathematics, QUANTUM BILLIARDS, POISSON STATISTICS. Year. Buy The Determination of the Scattering Potential From the Spectral Measure Function, Vol. 2: Point Eigenvalues and Proper Eigenfunctions (Classic Reprint) on . The trace formula relates the two-point spectral correlation function R 2 (x) to a sum over all pairs of periodic orbits. In the case of ‘generic’ graphs, standard semiclassical.
Specifically we have observed that for window sizes ranging between l%-7% of the length of a face of the square, the initial nonexponential era is practically the same (within thLe errors).Chaotic Billiards c I 20 40 60 80 L Figure 2. The decay of the correlation function A (t) as t evolves, Cited by: 2. With this motivation we study correlation functions for the motion of a point particle within a right triangular billiard, shaping it such that the acute angles are not rationally connected to 7r: otherwise global ergodicity would obviously fail, as the phase space is foliated by a family of invariant surfaces, Cited by: 6. arXivv2 [tangoloji.com] 14 Aug The n-level spectral correlations for chaotic systems Taro Nagao1 and Sebastian Mu¨ller2 1 Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya , Japan 2 Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK Abstract We study the n-level spectral correlation functions of classically. The spectral rigidity Delta(L) of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of L mean level spacings.
The spectral rigidity Delta(L) of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of L mean level tangoloji.com: Stefan Keppeler. Dec 09, · Classical transport in a doubly connected polygonal billiard, i.e. the annulus square billiard, is considered. Dynamical properties of the billiard flow with a fixed initial direction are analyzed by means of the moments of arbitrary order of the number of revolutions around the inner square, accumulated by the particles during the evolution. of the spectral density of its mean square value mean square value in frequency range: f, f f x 2 f, f = lim T ∞ 1 T ∫ 0 T x t, f, f 2 dt portion of x(t) in (f,f+∆f) x 2 f, f ≈ G definition of power spectral density function. BOUNDARY EFFECT ON THE NODAL LENGTH FOR ARITHMETIC RANDOM WAVES, AND SPECTRAL SEMI-CORRELATIONS VALENTINA CAMMAROTA1, OLEKSIY KLURMAN2, AND IGOR WIGMAN3 Dedicated to the memory ofAuthor: Valentina Cammarota, Oleksiy Klurman, Igor Wigman.