skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum chaos in nuclear physics

Abstract

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

Authors:
 [1]
  1. St. Petersburg State University (Russian Federation)
Publication Date:
OSTI Identifier:
22612640
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 79; Journal Issue: 4; Other Information: Copyright (c) 2016 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; CHAOS THEORY; DEGREES OF FREEDOM; HAMILTONIANS; LYAPUNOV METHOD; NUCLEAR PHYSICS; QUANTUM NUMBERS; QUANTUM SYSTEMS; SYMMETRY

Citation Formats

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu. Quantum chaos in nuclear physics. United States: N. p., 2016. Web. doi:10.1134/S1063778816040062.
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu. Quantum chaos in nuclear physics. United States. doi:10.1134/S1063778816040062.
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu. 2016. "Quantum chaos in nuclear physics". United States. doi:10.1134/S1063778816040062.
@article{osti_22612640,
title = {Quantum chaos in nuclear physics},
author = {Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu},
abstractNote = {A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.},
doi = {10.1134/S1063778816040062},
journal = {Physics of Atomic Nuclei},
number = 4,
volume = 79,
place = {United States},
year = 2016,
month = 7
}
  • 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 ensemblesmore » 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.« less
  • 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 implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoreticalmore » methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin and parity) and time-reversal invariance.« less
  • This article addresses the role of such concepts as chaos and predictability in the context of nuclear physics. The topic of this article is closely linked with such diverse areas as random-matrix theory, chaos in classical dynamical systems, statistical mechanics of small quantum systems, and the theory of disordered solids. We present recent information on nuclear data and on their analysis in terms of random-matrix models, a summary of work done on classical chaotic systems, on their quantum analogues, and on special systems like the hydrogen atom in a strong magnetic field. Also, we discuss how random-matrix models can bemore » used to simulate chaotic behaviour in small quantum systems, the role of symmetries (isospin, parity, and time-reversal) in chaotic quantum (nuclear) systems, and how chaos surfaces in experimental and theoretical investigations in molecular physics, in the physics of small clusters, and the analysis of conductance fluctuations in solids. (AIP)« less
  • The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in [sup 40]Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affect the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.
  • Using numerical simulations we investigate dynamical quantum chaos in isolated nuclear spin systems. We determine the structure of quantum states, investigate the validity of the Curie law for magnetic susceptibility and find the spectrum of magnetic noise. The spectrum is the same for positive and negative temperatures. The study is motivated by recent interest in condensed-matter experiments for searches of fundamental parity- and time-reversal-invariance violations. In these experiments nuclear spins are cooled down to microkelvin temperatures and are completely decoupled from their surroundings. A limitation on statistical sensitivity of the experiments arises from the magnetic noise.