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Characterization of chaotic quantum spectra and universality of level fluctuation laws
On trouve que les fluctuations de niveau du billard quantique de Sinai sont consistantes avec les predictions de l'ensemble orthogonal gaussien des matrices aleatoires
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Quantum chaotic dynamics and random polynomials
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 thatExpand
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Randomly incomplete spectra and intermediate statistics.
  • O. Bohigas, M. P. Pato
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and…
  • 7 August 2006
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitionsExpand
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Chaotic motion and random matrix theories
“Cada ciencia ha mester los vocables per los quals mills sia manifestada ; e car a aquesta c iencia ia demostrativa sien mester vocables s escurs e que los homens lecs no han en us, e cat nos facamExpand
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Missing levels in correlated spectra
Complete spectroscopy (measurements of a complete sequence of consecutive levels) is often considered as a prerequisite to extract fluctuation properties of spectra. It is shown how this goal can beExpand
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Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue isExpand
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Spectral properties of distance matrices
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.Expand
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Large deviations of the maximum eigenvalue in Wishart random matrices
We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show thatExpand
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Distributions of conductance and shot noise and associated phase transitions.
For a chaotic cavity with two identical leads each supporting N channels, we compute analytically, for large N, the full distribution of the conductance and the shot noise power and show that in bothExpand
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Fluctuation Properties of Nuclear Energy Levels and Widths : Comparison of Theory with Experiment
We analyze the fluctuation properties of nuclear energy levels and widths with new spectrally averaged measures. A remarkably close agreement between the predictions of random-matrix theories andExpand
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