Level spacing distribution of scissors mode states in heavy deformed nuclei

Collective vs. single-particle motion in quantum many-body systems: Spreading and its semiclassical interpretation in the perturbative regime

“…Owing to the harmonic form ofĤ 0 , we find the identity (15) for the commutator of the n-th powers of differences with the collective operator. For all n, it can be reduced to the operator (x…”

“…[14][15][16]. This coexistence of both regular and chaotic dynamics in the same system is a truly intriguing dynamical aspect of many-body systems [17].…”

Random matrix theory models of electric grid topology

“…Heavy nuclei are systems of many interacting nucleons and may be described by a Hamiltonian whose elements H ij are independent Gaussiandistributed random variables. (Nuclei are also capable of collective motions such as deformations or rotations [28,29]; here we will consider only the single-particle states.) Additionally, we expect the Hamiltonian to be invariant under some symmetries.…”

Doorway Mechanism in Many-Body Systems and in Quantum Billiards

“…Hence, the implicit assumption emerged that the doorway mechanism always comes with chaotic statistics of the background states. The analysis [9] of the magnetic analog of the GDR came as a considerable, entirely unexpected surprise: At low excitation energies, deformed nuclei can move just like a pair of scissors. The protons and neutrons in this scissors mode excitation (SME) can be viewed as confined in two ellipsoids which oscillate against each others as displayed in Fig.…”

“…They can be attributed to the SME by means of experimental information. Collecting data from different nuclei in the rare earth region, the level statistics was analyzed [9] and found to be regular. This is inherently incompatible with a doorway interpretation, since a coupling between doorway and background states is tantamount to the existence of correlations between the true eigenstates.…”