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Weidenmüller, H A, E-mail: Hans.Weidenmueller@mpi-hd.mpg.de

AbstractAbstract

[en] Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow. (paper)

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Available from http://dx.doi.org/10.1088/0954-3899/41/9/094010; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. G, Nuclear and Particle Physics; ISSN 0954-3899; ; CODEN JPGPED; v. 41(9); [8 p.]

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[en] We consider m spinless Bosons distributed over l degenerate single-particle states and interacting through a k-body random interaction with Gaussian probability distribution (the Bosonic embedded k-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as l→∞ or as m→∞. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit l→∞ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as m→∞ with both k and l fixed. Here we show that the ensemble is not ergodic and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency toward picket-fence-type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization

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S0003491602962536; 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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[en] The Hauser-Feshbach formula for the average compound-nucleus cross section formalizes Bohr's hypothesis of the independence of formation and decay of the compound nucleus. The statistical theory of compound-nuclear reactions aims at establishing the domain and limits of applicability of that formula and of Ericson's model for statistical cross section fluctuations using random-matrix theory as a starting point. I discuss the present status of that program, including the treatment of direct reactions

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CNR 2007: 2007 international workshop on compound-nuclear reactions and related topics; Yosemite National Park, CA (United States); 22-26 Oct 2007; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

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AbstractAbstract

[en] Because of the non-zero nuclear equilibration time, the compound-nucleus scattering model fails when the incident energy exceeds 10 or 20 MeV, and precompound reactions become important. Basic ideas used in the quantum-statistical approaches to these reactions are described

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CNR 2007: 2007 international workshop on compound-nuclear reactions and related topics; Yosemite National Park, CA (United States); 22-26 Oct 2007; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

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AbstractAbstract

[en] We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry

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4. conference on nuclei and mesoscopic physics 2014; East Lansing, MI (United States); 5-9 May 2014; (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

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Pluhař, Z; Weidenmüller, H A, E-mail: haw@mpi-hd.mpg.de

AbstractAbstract

[en] For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas–Giannoni–Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every $(P,Q)$ correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron–Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron–Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size. (paper)

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Available from http://dx.doi.org/10.1088/1751-8113/48/27/275102; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121; ; v. 48(27); [30 p.]

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Papenbrock, T; Weidenmüller, H A, E-mail: tpapenbr@utk.edu, E-mail: haw@mpi-hd.mpg.de

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[en] We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field. (invited comment)

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Available from http://dx.doi.org/10.1088/0031-8949/91/5/053004; Country of input: International Atomic Energy Agency (IAEA)

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Physica Scripta (Online); ISSN 1402-4896; ; v. 91(5); [12 p.]

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[en] The embedded ensembles were introduced by Mon and French (1975 Ann. Phys., NY 95 90) as physically more plausible stochastic models of many-body systems governed by one- and two-body interactions than provided by standard random-matrix theory. We review several approaches aimed at determining the spectral density, the spectral fluctuation properties and the ergodic properties of these ensembles: moments methods, numerical simulations, the replica trick, the eigenvector decomposition of the matrix of second moments and supersymmetry, the binary correlation approximation, and the study of correlations between matrix elements

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S0305-4470(03)40063-2; Available online at http://stacks.iop.org/0305-4470/36/3569/a31240.pdf or at the Web site for the Journal of Physics. A, Mathematical and General (ISSN 1361-6447) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. A, Mathematical and General; ISSN 0305-4470; ; v. 36(12); p. 3569-3593

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Papenbrock, T; Weidenmüller, H A, E-mail: tpapenbr@utk.edu, E-mail: haw@mpi-hd.mpg.de

AbstractAbstract

[en] Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. We extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. In deformed nuclei these are vibrational modes each of which serves as band head of a rotational band. (paper)

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Available from http://dx.doi.org/10.1088/0954-3899/42/10/105103; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. G, Nuclear and Particle Physics; ISSN 0954-3899; ; CODEN JPGPED; v. 42(10); [33 p.]

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AbstractAbstract

[en] Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.

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(c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

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