VARs with Mixed Roots Near Unity

Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity -- in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.Common roots, Local to unity, Mildly explosive, Mixed roots, Model selection, Persistence, Tests of common roots

Effective field theory description of halo nuclei

Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the core and the valence nucleons. Similar phenomena occur in clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some exotic hadrons. In these weakly-bound quantum systems universal scaling laws for s-wave binding emerge that are independent of the details of the interaction. Effective field theory (EFT) exposes these correlations and permits the calculation of non-universal corrections to them due to short-distance effects, as well as the extension of these ideas to systems involving the Coulomb interaction and/or binding in higher angular-momentum channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo nuclei, has been used to compute the properties of single-neutron, two-neutron, and single-proton halos of s-wave and p-wave type. This review summarizes these results for halo binding energies, radii, Coulomb dissociation, and radiative capture, as well as the connection of these properties to scattering parameters, thereby elucidating the universal correlations between all these observables. We also discuss how Halo EFT's encoding of the long-distance physics of halo nuclei can be used to check and extend ab initio calculations that include detailed modeling of their short-distance dynamics.Comment: 104 pages, 31 figures. Topical Review for Journal of Physics G. v2 incorporates several modifications, particularly to the Introduction, in response to referee reports. It also corrects multiple typos in the original submission. It corresponds to the published versio

Quantum Monte Carlo Study of Disordered Fermions

We study a strongly correlated fermionic model with attractive interactions in the presence of disorder in two spatial dimensions. Our model has been designed so that it can be solved using the recently discovered meron-cluster approach. Although the model is unconventional it has the same symmetries of the Hubbard model. Since the naive algorithm is inefficient, we develop a new algorithm by combining the meron-cluster technique with the directed-loop update. This combination allows us to compute the pair susceptibility and the winding number susceptibility accurately. We find that the s-wave superconductivity, present in the clean model, does not disappear until the disorder reaches a temperature dependent critical strength. The critical behavior as a function of disorder close to the phase transition belongs to the Berezinsky-Kosterlitz-Thouless universality class as expected. The fermionic degrees of freedom, although present, do not appear to play an important role near the phase transition.Comment: published version, more data added to Fig 5 and clarifications in text, 8 page

Implications of a matter-radius measurement for the structure of Carbon-22

We study Borromean 2n-halo nuclei using effective field theory. We compute the universal scaling function that relates the mean-square matter radius of the 2n halo to dimensionless ratios of two- and three-body energies. We use the experimental value of the rms matter radius of 22C measured by Tanaka et al. to put constraints on its 2n separation energy and the 20C-n virtual energy. We also explore the consequences of these constraints for the existence of excited Efimov states in this nucleus. We find that, for 22C to have an rms matter radius within 1-sigma of the experimental value, the two-neutron separation energy of 22C needs to be below 100 keV. Consequently, this three-body halo system can have an excited Efimov state only if the 20C-n system has a resonance within 1 keV of the scattering threshold.Comment: 6 pages, 4 figure

Drell-Hearn-Gerasimov Sum-Rule for the Deuteron in Nuclear Effective Field Theory

The Drell-Hearn-Gerasimov sum rule for the deuteron is studied in nuclear effective field theory. The low-energy theorem for the spin-dependent Compton amplitude $f_1(\omega)$ is derived to the next-to-leading order in low-energy expansion. The spin-dependent photodisintegration cross section $\sigma^P-\sigma^A$ is calculated to the same order, and its contribution to the dispersive integral is evaluated.Comment: 8 pages, 2 figure

Range Corrections to Three-Body Observables near a Feshbach Resonance

A non-relativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length a is much larger than the range l of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the |a| goes to infinity limit and finite-l/a corrections to observables of interest. Here we use such an effective-theory treatment to consider the impact of corrections linear in the two-body effective range, r_s on the three-boson bound-state spectrum and recombination rate for |a| much greater than |r_s|. We do this by first deriving results appropriate to the strict limit |a| goes to infinity in coordinate space. We then extend these results to finite a using once-subtracted momentum-space integral equations. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.Comment: 28 pages, 3 figure