1k citations · 2.3k across the 40 of their papers we have counts for
8 papers · 1 filter
Statistical properties of structured random matrices
Eugene Bogomolny, Olivier Giraud
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical a…
Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
E. Bogomolny, M. Sieber
The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments re…
Modification of the Porter-Thomas distribution by rank-one interaction
E. Bogomolny
The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed…
Scattering om two Aharonov-Bohm vortices
Eugene Bogomolny
The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed in [J. M. Myers, J. Math. Phys. \textbf…
Quantum Ising model in transverse and longitudinal fields: chaotic wave functions
Y. Y. Atas, E. Bogomolny
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of…
Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations
Y. Y. Atas, E. Bogomolny
Spectral density of quantum Ising model in two fields for large but finite number of spins , is discussed in detail. When all coupling constants are of the same order, spectral…
The distribution of the ratio of consecutive level spacings in random matrix ensembles
Y. Y. Atas, E. Bogomolny, O. Giraud +1
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was re…
Painleve solution of an integral equation
Y. Y. Atas, E. Bogomolny
It is demonstrated that a certain integral equation can be solved using the Painleve equation of third kind. Inversely, a special solution of this Painleve equation can be expresse…