Understanding chaos via nuclei

Abstract

We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.

Spectral statistics of rare-earth nuclei: Investigation of shell model configuration effect

“…In this paper, we consider the statistical properties of even-even rare earth nuclei. With regard to complete theoretical studies [30][31][32][33][34][35][36][37][38][39][40][41] and also the experimental evidences [31][32][33], we tend to classify nuclei in different categories. We considered all isotopes of Ba, Ce, Nd, Sm, Gd, Dy, Er, Yb and Hf nuclei which have at least five consecutive levels with definite spin-parity J π assignment as presented in Table 1.…”

Quantum phases and entanglement properties of an extended Dicke model

“…The way how the regular fraction is obtained from numerical simulation of classical dynamics is described in Ref. [41]. The evolution of the classical regular fraction for Hamiltonian (8) with δ increasing from 0 to 1 is shown in Fig.…”

Study of a curvature-based criterion for chaos in Hamiltonian systems with two degrees of freedom

“…As shown in [17,23], the classical Bohr Hamiltonian exhibits a very sophisticated interplay of regular and chaotic features. This also quantified its quantized version to be used in numerous theoretical analyzes related to quantum chaos [24][25][26][27][28][29].…”

“…In this work, the values of f E reg are calculated numerically with the aid of a sample of randomly selected trajectories whose stability properties are determined by a method based on so-called alignment indices [30]. For more details on the evaluation of f E reg , see [29]. The η × E map of classical chaos for Hamiltonian (15) is depicted in figure 1.…”