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- E Bogomolny, O Bohigas, P Leboeuf
- 1996

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of " quantum chaotic dynamics ". It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study… (More)

- E Bogomolny, F Leyvraz
- 1996

The two-point correlation functions of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions , are explicitly computed using a generalization of the Hardy– Littlewood method. It is shown that in the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but… (More)

- E Bogomolny, O Bohigas, C Schmit
- 2003

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)

- E B Bogomolny, M Carioli
- 1993

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)

- Eugene Bogomolny
- 2003

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)

- E Bogomolny, U Gerland, C Schmit
- Physical review. E, Statistical, nonlinear, and…
- 2001

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)

- E Bogomolny, R Dubertrand, C Schmit
- 2006

The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE 6 curves which describe the continuum limit of the percolation cluster boundaries. This result gives an additional support to the recent conjecture that the nodal domains of random (and chaotic) wave functions in the… (More)

- E. Bogomolny, M. Huleihel, Y. Suproun, R. K. Sahu, S. Mordechai, Shaul Mordechai
- 2006

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)

- E Bogomolny, N Pavloff, C Schmit
- 2008

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)

- Eugène Bogomolny
- 2008

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)