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40 papers
Level compressibility of certain random unitary matrices
Eugene Bogomolny
The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of…
Random matrices associated with general barrier billiards
Eugene Bogomolny
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensiona…
Barrier billiard and random matrices
Eugene Bogomolny
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonst…
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…
Formation of superscar waves in plane polygonal billiards
Eugene Bogomolny
Polygonal billiards constitute a special class of models. Though they have zero Lyapunov exponent their classical and quantum properties are involved due to scattering on singular…
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…