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Quantum and Arithmetical Chaos
Eugene Bogomolny
The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and…
Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models
Eugene Bogomolny, Charles Schmit
Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle groups are discussed. It is demonstrated both numerically and analytically that at least for certain grou…
Asymptotic behaviour of multiple scattering on infinite number of parallel demi-planes
Eugene Bogomolny, Charles Schmit
The exact solution for the scattering of electromagnetic waves on an infinite number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins in 1947 using the Wien…
Spectral properties of distance matrices
E. Bogomolny, O. Bohigas, C. Schmit
Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one…