Random Matrices and Chaos in Nuclear Physics

By H. A. Weidenmüller, G. Mitchell. 2008

208 citations recorded by the source corpus.

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 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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2f2640ef13ae9cd677f7a7ce6031b18f13ae3cfb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. L. Grigorenko
2. M. Pfützner
3. Sylvain Gigan
4. Karsten Riisager
5. Kristiaan Heyde
6. S. Rotter
7. M. Karny

In Statistical and Nonlinear Physics

1. Sylvain Gigan
2. S. Rotter

Citations in the corpus

• Light fields in complex media: Mesoscopic scattering meets wave control (2017, background): “…spacings in nuclei (Wigner, 1955a), has meanwhile found a broad range of applications, not only in nuclear physics (see (Mitchell et al., 2010; Weidenmüller and Mitchell, 2009) for a review), but also in mesoscopic physics (see (Beenakker, 1997) for a review) and increasingly so in…”
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles (2016, background): “es of many-body quantum chaos mainly used the so-called “nuclear data ensemble” of neutron resonance data [132, 133]. Later a broad material from large-scale atomic and nuclear many-body calculations [35, 134, 1, 135] was added to the discussion that gave an impulse to return [1, 136] to the problem”
• Radioactive decays at limits of nuclear stability (2011, background): “As it increases the local structure changes from rather regular to essentially chaotic, a transition well-studied theoretically but experimentally less understood in nuclei (Weidenmüller and Mitchell, 2009).”
• Magnetic dipole excitations in nuclei: Elementary modes of nucleonic motion (2010, background): “This complexity has led Wigner, more than forty years ago, to the introduction of Random Matrix Theory (RMT), reviewed in detail by Guhr et al. (1998) and Weidenmüller and Mitchell (2009).”