E 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)
It has been conjectured that the statistical properties of zeros of the Riemann zeta function near z = 1/2 + iE tend, as E → ∞, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite E numerical results show that the nearest-neighbour spacing distribution presents deviations with respect to the conjectured(More)
The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with a pointlike scatterer inside for periodic and Dirichlet boundary conditions, and it is demonstrated that when s-->infinity this function decreases exponentially. Together with the results of Bogomolny, Gerland, and Schmit [Phys. Rev. E 63,(More)
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)
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)
The computation of the two-point correlation form factor K(τ) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation expansion of this form factor in powers of τ can be computed directly from a semiclassical trace formula. The main part(More)