Eugène Bogomolny

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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 are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The(More)
The Selberg zeta function S (s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic ow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, S (s) can be exactly(More)
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 of the Laplace–Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical(More)
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically, and explicit calculations are performed for the two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation(More)
Fourier transform infrared Microspectroscopy (FTIR-MSP) is potentially a powerful analytical method for identifying the spectral properties of biological activity in cells. The goal of the present research is the implementation of FTIR-MSP to study early spectral changes accompanying malignant transformation of cells. As a model system, cells in culture(More)
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction typically occurs at the boundary of a family of trajectories. In this case the first diffractive correction to the contribution of the family to the periodic orbit expansion is(More)
A brief review of recent developments in the theory of the Riemann zeta function inspired by ideas and methods of quantum chaos is given. At the first glance the Riemann zeta function and quantum chaos are completely disjoint fields. The Riemann zeta function is a part of pure number theory but quantum chaos is a branch of theoretical physics devoted to the(More)