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E Bogomolny

Publications and source records attributed to E Bogomolny.

6 recordsLinked to original sources
PubMed2002

Nearest-neighbor distribution for singular billiards.

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, 036206 (2001)], it proves that spectral statistics of such systems is of intermediate type characterized by level repulsion at small distances and exponential fall-off of the nearest-neighbor distribution at large distances. The calculation of the nth nearest-neighbor spacing distribution P(n)(s) and its asymptotics is performed as well for any boundary conditions.

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PubMed2002

Percolation model for nodal domains of chaotic wave functions.

Nodal domains are regions where a function has definite sign. In [] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolationlike model for description of these nodal domains which permits us to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way to deeper understanding of the structure of chaotic wave functions.

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PubMed2001

Singular statistics.

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 of an integrable Hamiltonian and, in particular, when a delta-function potential is added to an integrable billiard.

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PubMed2000

Spectral statistics of chaotic systems with a pointlike scatterer

The statistical properties of a Hamiltonian H0 perturbed by a localized scatterer are considered. We prove that if H0 describes a bounded chaotic motion, the universal part of the spectral statistics is not changed by the perturbation. This is done first within the random matrix model. Then it is shown by semiclassical techniques that the result is due to a cancellation between diagonal diffractive and off-diagonal periodic-diffractive contributions. The compensation is a very general phenomenon encoding the semiclassical content of the optical theorem.

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PubMed2000

Diffractive corrections in the trace formula for polygonal billiards

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 of order of that of an isolated orbit, and gives the first sqrt[Planck's over 2pi] correction to the leading semiclassical term. Keller's geometrical theory of diffraction is inadequate for treating these corrections and we develop an alternative approximation based on Kirchhoff's theory. Numerical checks show that our procedure allows reduction of the typical semiclassical error by about two orders of magnitude. The method permits treatment of the related problem of flux-line diffraction with the same degree of accuracy.

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