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Khuat-duy, D.; Leboeuf, P.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] One-dimensional asymmetric double-well potentials of degree four have the property that, at a fixed energy, the classical period is the same in both wells. It is shown that at the quantum level this property reflects in an alignment of the spectral quasi-degeneracies at certain values of the parameters controlling the form of the potential. Experimental applications of this property are discussed. (author) 7 refs.; 5 figs

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Jul 1992; 16 p

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Leboeuf, P.; Mouchet, A.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] The dispersion laws of chaotic periodic systems are computed using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, complex orbits are also included. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime. (authors). 14 refs., 1 fig

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Apr 1994; 12 p

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[en] We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the thermodynamic function considered, and on temperature, we find that the probability distributions are dominated either (i) by the local fluctuations of the single-particle spectrum on the scale of the mean level spacing, or (ii) by the long-range modulations of that spectrum produced by the short periodic orbits. In case (i) the probability distributions are computed using the appropriate local universality class, uncorrelated levels for integrable systems, and random matrix theory for chaotic ones. In case (ii) all the moments of the distributions can be explicitly computed in terms of periodic orbit theory and are system-dependent, nonuniversal, functions. The dependence on temperature and on number of particles of the fluctuations is explicitly computed in all cases, and the different relevant energy scales are displayed

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S0003491602962469; Copyright (c) 2002 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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Bogomolny, E.; Leboeuf, P.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] The statistical distribution of the zeros of Dirichlet L-functions is investigated both analytically and numerically. Using the Hardy-Littlewood conjecture about the distribution of primes it is shown that the two-point correlation function of these zeros coincides with that for eigenvalues of the Gaussian unitary ensemble of random matrices, and that the distributions of zeros of different L-functions are statistically independent. Applications of these results to Epstein's zeta functions are shortly discussed. (authors) 30 refs., 3 figs., 1 tab

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Sep 1993; 26 p

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Bogomolny, E.; Bohigas, O.; Leboeuf, P.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] The distribution of roots of polynomials of high degree with random coefficients is investigated 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, the particular case of self-inverse random polynomials is studied, and it is shown that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials. (author)

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Nov 1995; [40 p.]; 32 refs.

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Leboeuf, P.; Monastra, A.G., E-mail: leboeuf@ipno.in2p3.fr

AbstractAbstract

[en] We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully chaotic classical dynamics. The probability distributions of the quantum fluctuations of the grand potential and entropy of the gas are computed as a function of temperature and compared, with good agreement, with general predictions obtained from random matrix theory and periodic orbit theory (based on prime numbers). In each case the universal and non-universal regimes are identified

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S0375947403014738; Copyright (c) 2003 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: Canada

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Bernath, M.; Fendrik, A.J.; Leboeuf, P.; Perazzo, R.P.J.; Saraceno, M.

Proceedings of the 10. Workshop on Nuclear Physics in Brazil

Proceedings of the 10. Workshop on Nuclear Physics in Brazil

AbstractAbstract

[en] Published in summary form only

Original Title

El billar eliptico rotante: un problema de interes para la fisica nuclear

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Sociedade Brasileira de Fisica, Sao Paulo; 172 p; 1987; p. 77; 10. Workshop on Nuclear Physics in Brazil; Caxambu, MG (Brazil); 26-30 Aug 1987

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Miscellaneous

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Leboeuf, P.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. The diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map is computed analytically. The variations of the transport coefficient as a parameter is varied are analyzed in terms of the underlying classical trajectories with particular emphasis in the appearance and bifurcations of periodic orbits. When accelerator modes are present, anomalous diffusion of the Levy type can occur. The exponent characterizing the anomalous diffusion is computed numerically and analyzed as a function of the parameter. (author)

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Nov 1996; [21 p.]; 24 refs.

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Faure, F.; Leboeuf, P.

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

AbstractAbstract

[en] The quantum eigenstates and eigenvalues on a toroidal two dimensional phase-space are studied. To each eigenfunction is associated an integer, the Chern index, which tests the localization of the eigenfunction as some periodicity conditions are changed. The Chern index is a topological invariant which can only change when a spectral degeneracy occurs. These topological numbers are computed for three different models: two having an underlying regular dynamics, the third-one having a chaotic dynamics. The role played by the separatrix-states, the effects of quantum tunneling (symmetry effects) and of a classically chaotic dynamics in the spectrum of the Chern indices are discussed. The values taken by those indices are interpreted in terms of a phase-space distribution function. (author) 13 refs.; 12 figs

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Oct 1992; 25 p; From classical to quantum chaos workshop; Trieste (Italy); 21-24 Jul 1992

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[en] We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of open-quotes quantum chaotic dynamics.close quotes 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 in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials

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