Related papers: Comment on `Two-body random ensembles: from nuclea…
The two-body random ensemble (TBRE) for a many-body bosonic theory is mapped to a problem of random polynomials on the unit interval. In this way one can understand the predominance of 0+ ground states, and analytic expressions can be…
Combining analytical and numerical methods, we investigate properties of the two-body random ensemble (TBRE). We compare the TBRE with the Gaussian orthogonal ensemble of random matrices. Using the geometric properties of the nuclear shell…
We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation.Surprisingly we find patterns reminiscent of more orderly interactions,…
It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one…
Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational…
We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with random two-body interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities…
We investigate the phenomenom of emerging regular spectral features from random interactions. In particular, we address the dominance of L=0 ground states in the context of the vibron model and the interacting boson model. A mean-field…
The predictions of the IBM two-body random ensemble are compared to empirical results on nuclei from Z=8 to 100. Heretofore unrecognized but robust empirical trends are identified and related both to the distribution of valence nucleon…
Using longer spectra we re-analyze spectral properties of the two-body random ensemble studied thirty years ago. At the center of the spectra the old results are largely confirmed, and we show that the non-ergodicity is essentially due to…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the…
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one- and two-body interactions. Despite the randomness of the interactions (in sign and size)…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
A variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the…
We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…
The input to the configuration-interaction shell model includes many dozens or hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to…
We study the origin of the regular features obtained in numerical studies of the IBM with random interactions, in particular the dominance of L=0 ground states and the occurrence of vibrational and rotational band structures. It is shown…