The problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the Δ3 statistic.The problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the Δ3 statistic.

AIP conference proceedingsJan 1, 20170 citations

Extraction of quantum randomness

Igor M. Arbekov, S. N. Molotkov

Uspekhi Fizicheskih NaukNov 1, 202016 citations

Quantum chaos in ultracold collisions between Yb(1S0) and Yb(3P2)

Dermot G. Green, Christophe L. Vaillant, Matthew D. Frye +2 more

We calculate and analyze Feshbach resonance spectra for ultracold $\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})$ collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.We calculate and analyze Feshbach resonance spectra for ultracold $\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})$ collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

arXiv:1510.06992Physical Review AFeb 4, 201617 citations

Complexity of Quantum Spectra

Yuri A. Dabaghian

APSMar 1, 20050 citations

We calculate and analyze Feshbach resonance spectra for ultracold

\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})

collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.