Regularities of many-body systems interacting by a two-body random ensemble

Abstract

The ground states of all even-even nuclei have angular momentum, I, equal to zero, I = 0, and positive parity, π = +. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of I π = 0 + ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-j shells for small j, there are a few approaches to predict and/or explain spin I ground state (I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single-j (j > 7/2) or many-j shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of manybody systems in the presence of random two-body interactions, such as the odd-even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced twobody random ensemble.

Two-body random ensemble in nuclei

“…Our calculations are partly based on the shell-model code Oxbash [10]. The square roots s α (J) for 20 Ne are shown in Fig. 3, those for 24 Mg are shown in Fig.…”

“…Subsequent work showed that similar regularities exist in bosonic [17] and electronic [18] many-body systems with two-body interactions. The phenomenon of spin-zero preponderance seems a robust and rather generic feature which has received much attention since, see the reviews [19,20] and references therein. Here we discuss it in the framework of our representation (9) of the Hamiltonian of the TBRE.…”

“…Correlations are also expected to exist between states in different nuclei when these are governed by the same TBRE. A case in point are the T = 0 spin zero states in 20 Ne and 24 Mg. Their correlations are shown in Figure 12 where we use the same display as in Figure 11. Again, we find weak correlations of the order of several percent.…”

Recent progress in theoretical nuclear physics related to large-scale scientific facilities

“…The randomness of matrix elements of the nuclear shell model Hamiltonian is an interesting topic [81][82][83]. Shen et al studied the general behavior of matrix elements of the nuclear shell model Hamiltonian [84].…”

Eigenvalue correlations and the distribution of ground state angular momenta for random many-body quantum systems

“…The observation of a statistical preference of L = 0 ground states for ensembles of random two-body interactions has sparked a large number of investigations to further explore the properties of these random systems and to understand the mechanism for the emergence of regular ordered spectral features from random interactions [6][7][8][9]. The appearance of ordered spectra in systems with chaotic dynamics is a robust property that does not depend on the specific choice of the (two-body) ensemble of random interactions [2,[10][11][12], timereversal symmetry [10], and the restriction of the Hamiltonian to one-and two-body interactions [13], nor is it limited to yrast states with small angular momentum L = 0, 2, 4 [14] as used in the original studies [2,3].…”