Related papers: Random Matrices and Chaos in Nuclear Physics
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…
The presence of quantum chaos in nuclear mass systematics is analyzed by considering the differences between measured and calculated nuclear masses as a time series described by the power law 1/ f^alpha. While for the liquid droplet model…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
In atomic nuclei, as in other many-body systems, the classical phase space is mixed, so ordered and chaotic states generally coexist. In this contribution we discuss some models, showing the transition from order to chaos. In several cases…
Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with…
Using a classical analytical criterion (that of curvature) and numerical results (Poincar\`e sections and spectral statistics), a transition order--chaos--order in the roto--vibrational model of atomic nuclei has been shown. Numerical…
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…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
This is a continuation of our preceding paper devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as…
We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting…
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…
The issue of averaging randomness is addressed, mostly in nuclear physics, but shortly also in QCD. The Feshbach approach, so successful in dealing with the continuum spectrum of the atomic nuclei ("optical model"), is extended to encompass…
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…
We propose a novel method for analysis of experimental data obtained at relativistic nucleus-nucleus collisions. The method, based on the ideas of Random Matrix Theory, is applied to detect systematic errors that occur at measurements of…
The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The…
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…