TY - JOUR
T1 - Models of intermediate spectral statistics
AU - Bogomolny, E. B.
AU - Gerland, U.
AU - Schmit, C.
PY - 1999
Y1 - 1999
N2 - Based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the Anderson model at the transition point. A simple theoretical model where such statistics can be obtained analytically is briefly discussed. A few models with similar behavior are considered. In particular, we analytically found the eigenvalue statistics of a Poisson-distributed matrix perturbed by a rank one matrix, which is a good model for spectral statistics of a singular billiard.
AB - Based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the Anderson model at the transition point. A simple theoretical model where such statistics can be obtained analytically is briefly discussed. A few models with similar behavior are considered. In particular, we analytically found the eigenvalue statistics of a Poisson-distributed matrix perturbed by a rank one matrix, which is a good model for spectral statistics of a singular billiard.
UR - http://www.scopus.com/inward/record.url?scp=85035206212&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.59.R1315
DO - 10.1103/PhysRevE.59.R1315
M3 - Article
AN - SCOPUS:85035206212
SN - 1063-651X
VL - 59
SP - R1315-R1318
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 2
ER -