Structure of compound states in the chaotic spectrum of the Ce atom: Localization properties, matrix elements, and enhancement of weak perturbations

Abstract

The aim of the present paper is to analyze a realistic model of a quantum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic con6gurationinteraction method the spectra and the wave functions of odd and even levels of Ce with J = 4 are calculated. It is shown that the structure of the excited states at excitation energies above 1 eV becomes similar to that of the compound states in heavy nuclei. The wave functions of the excited states are chaotic superpositions of the simple basis states (with the number of "principal" components N 100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigenstates on the energy scale is characterized by the spread width I' ND, where D is the average level spacing (D 0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and I parameters on the excitation energy are studied. The shape of the localization is shown to be Lorenzian around the maximum (principal components), whereas outside this region the squared components display a faster decrease, in agreement with the perturbation theory treatment of the band random matrix (BRM) model. The structure of the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elements between the eigenstates in terms of their parameters and single-particle occupancies is derived, and its applicability is checked with the results of numerical calculations. The hypothesis of a Gaussian distribution of the eigenstates' components and matrix elements between the eigenstates has been checked. The existence of the statistical (dynamical) enhancement of weak perturbations in systems with dense spectra is demonstrated.

Quantum chaos in many-body systems: what can we learn from the Ce atom?

“…He studied configuration compositions of the eigenstates of the Ce atom using data from the tables [29], and came to the conclusion that the "eigenfunctions are random superpositions of some few basic states". Inspired by that work we conducted an extensive numerical study of the spectra and eigenstates of complex open-shell atoms, using the rare-earth atom of Ce as an example [8,16,[30][31][32]. The present paper summarizes our earlier findings, as well as gives new insights into the problem of quantum chaos in a real many-body system.…”

“…In our earlier work [8] we considered only a few lowest nonrelativistic configurations constructed of the 4f, 6s, 5d, and 6p orbitals, and had 260 and 276 eigenstates of the J π = 4 − and 4 + symmetries, respec- [29]. Thin solid line is the independent-particle fit (4).…”

“…(5). The spectral statistics were checked for many experimental and calculated complex atomic spectra [6][7][8][33][34][35], as well as for molecular vibronic spectra [36]. On the inset in Fig.…”

“…1 Studies of experimental data for the energy levels in heavy nuclei [5] and complex atoms [6,7] agree with the Wigner statistics. They have been observed in numerical calculations for the atom of cerium (Ce) [8] and the nuclear sd shell model [9][10][11][12].…”

Nuclear structure, random interactions and mesoscopic physics

“…From a more general theoretical viewpoint related to many-body quantum chaos [9,10,11], we deal with closed mesoscopic systems that generically display chaotization of motion due to intrinsic interactions. In the absence of a heat bath and external disorder, the interactions play the role of a randomizing or thermalizing factor.…”