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- Eugène Bogomolny, Charles Schmit
- Physical review letters
- 2002

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… (More)

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.… (More)

We review the relations between distance matrices and isometric embed-dings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one… (More)

- Eugène Bogomolny, Oriol Bohigas, P. Lebœuf
- 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… (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… (More)

- Eugène Bogomolny, N. Djellali, +5 authors Joseph Zyss
- Physical review. E, Statistical, nonlinear, and…
- 2011

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula… (More)

- Eugène Bogomolny, Charles Schmit
- Physical review letters
- 2004

Wave functions of pseudointegrable plane polygonal billiards are investigated. It is demonstrated that they have clear structures (superscars) related with families of classical periodic orbits which… (More)

- Eugène 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… (More)

- Eugène Bogomolny
- Chaos
- 1992

The dynamical zeta function is usually defined as an infinite (and divergent) product over all primitive periodic orbits. It is possible to show that as variant Planck's over 2pi -->0 it can be… (More)

- Yunus Atas, Eugène Bogomolny, Olivier Giraud, Guillaume Roux
- Physical review letters
- 2013

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced… (More)