相关论文: Random matrices, symmetries, and many-body states
Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise…
In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I…
Shell model calculations using realistic interactions reveal that the ground and low-lying yrast states of the $N=Z$ nucleus $^{92}_{46}$Pd are mainly built upon isoscalar neutron-proton pairs each carrying the maximum angular momentum J=9…
We use a single j-shell model with random two-body interactions to derive closed expressions for the distribution of and the correlations between spectral widths of different spins. This task is facilitated by introducing two-body operators…
The ground state correlations induced by a general pairing Hamiltonian in a finite system of like fermions are described in terms of four-body correlated structures (quartets). These are real superpositions of products of two pairs of…
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax…
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 classical ground state of a D- dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body…
The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be…
Optimization of quantum states using the variational principle has recently seen an upsurge due to developments of increasingly expressive wave functions. In order to improve on the accuracy of the ans\"atze, it is a time-honored strategy…
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,…
Binding energies, quadrupole deformation parameters, spins and parities of the neutron-deficient odd $Z=N+1$ nuclei in the $A\sim 80$ region are calculated in the relativistic mean field approximation. The ground-state and low-lying…
We prove a theorem that shows the degeneracy of many-body states depends on total particle number and flux filling ratio, for particles in a periodic lattice and under a uniform magnetic field. Non-interacting fermions and weakly…
We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A…
For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $\alpha^J_{I(v \beta)} = <nv \beta I |$ $A^{J \dagger} \cdot A^J | n v\beta I>$, where $n$…
We show that fully aligned neutron-proton pairs play a crucial role in the low-energy spectroscopy of nuclei. with valence nucleons in a high-j orbital. Their dominance is valid in nuclei with valence neutrons and protons in different…
Quantum systems with SU($N$) symmetry are paradigmatic settings for quantum many-body physics. They have been studied for the insights they provide into complex materials and their ability to stabilize exotic ground states. Ultracold…
The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we…
With a certain approximation for the Coulomb matrix elements in a single j shell of protons and neutrons it is found that wave functions of states of odd angular momentum J in an even-even nucleus are not strongly affected by their…
We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In…