Spectral Statistics of Irrational Polygonal Billiards
الكلمات المفتاحية:
Quantum Chaos، Green function، Helmholtz equation، Polygonal Billiards، Nearest neighbour spacing distributionالملخص
We investigate some statistical features of the spectrum related to the dynamical nature of the trajectories such as the fluctuation and the spacing between neighboring energy levels for polygonal billiard with some angles being irrational multiples of p.This addresses the effect of the polygonal geometry on the computed spectrum. .
المراجع
H. Stöckman, Quantum Chaos: An Introduction, Cambridge University, (1999).
G. Tanner and N Søndergaard, Wave Chaos in Acoustics and Elasticity, J. Phys. A,
, R443 (2007a).
T. Jonckheere, B.Grémaud, and D. Delande, Spectral Properties of Nonhydrogenic Atoms in Weak External Fields, Phys. Rev. letters, 81, 12, 2442—2445 (1998).
P.Richens, and M. Berry, Pseudo-integrable systems in classical and quantum mechanics, Physica 1D, 495-512, (1981).
E. B. Bogomolny, U. Gerland, and C. Schmit, Models of intermediate spectral statistics, Phys. Rev. E, 59, 2, (1999).
Y. Hlushchuk, A. BÇedowski, N. Savytskyy and L. Sirko , Numerical Investigation of Regimes of Wigner and ShnirelmanErgodicity in Rough Billiards , PhysicaScripta64, 192–169 (2001).
C.A. Brebbia, J.C.F.Telles, and L. C. Wrobel.Boundary element techniques, Springer-Verlag, Berlin and New York, 1984.
C.A. Brebbia, Walker, The boundary element techniques in engineering, Newnas- Butterworths, London, 1979.
M. Abramowitz and A. Stegun, Handbook of Mathematical Functions, New York: Dover Publications, Inc., (1968).
R. Kress,Linear Integral Equations, Applied Mathematical Sciences; Vol. 82, Springer-Verlag, New York, Inc., second edition,(1999).
P. A. Boasman, Semiclassical Accuracy for Billiards, Rev. Modern Phys.74 (1992).
E. Bogomolny and E. Huges, Semiclassical Theory of Flexural Vibration of Plates,
Phys. Rev. A, 57, 4, 5404 (1998).
