Related papers: Random Matrices and Chaos in Nuclear Spectra
The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix…
To elucidate the mechanism by which chaos is generated in the shell model, we compare three random-matrix ensembles: the Gaussian orthogonal ensemble, French's two-body embedded ensemble, and the two-body random ensemble (TBRE) of the shell…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
Shell effects in atomic nuclei are a quantum mechanical manifestation of the single--particle motion of the nucleons. They are directly related to the structure and fluctuations of the single--particle spectrum. Our understanding of these…
A statistical analysis of the spectrum of two particle - two hole doorway states in a finite nucleus is performed. On the unperturbed mean-field level sizable attractive correlations are present in such a spectrum. Including particle-hole…
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…
Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean field basis to…
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is…
The presence of chaos and quantum chaos is shown in two different nuclear systems. We analyze the chaotic behaviour of the classical SU(2) Yang--Mills--Higgs system, and then we study quantum chaos in the nuclear shell model calculating the…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest…
Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
In this work, the term ``quantum chaos'' refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using e.g.~the spectral form factor, which…
We discuss the role of quantum chaos in atomic nuclei. After reviewing the basic assumptions of the nuclear shell model, we analyze the spectral statistics of the energy levels obtained with realistic shell-model calculations in the fp…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to…
The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The…