Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.Comment: Some clarifications were added in the introduction and an extra appendix was adde

A comment on "What catch data can tell us about the status of global fisheries"

There is considerable interest in the state of the world’s natural fishery resources. The paper by Froese et al. (2012) is a recent example of applying a set of ad hoc decision rules to a time series of catch data in order to assign the world’s fisheries to categories of exploitation and hence make generalisations about their current status. They conclude that the percentage of stocks that are over-exploited is worse than previously reported in FAO (2010). The approach used by Froese et al. is based on an algorithm proposed by Froese and Kesner-Reyes (2002) which has been heavily criticised both on theoretical grounds and from simulation studies (Branch et al. 2011; Daan et al. 2011; Wilberg and Miller 2007). In their recent paper, Froese et al. (2012) produce additional analyses to support their method which assumes that maximum sustainable yield (MSY) lies in the interval (0.5Cmax, Cmax), where Cmax is the maximum observed catch in the time series. Unfortunately, these analyses do not support their contention that MSY for a particular stock is related to maximum catch in a predictable way and renders their conclusions unsaf

Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials or AREPs) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely non-local behaviour resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.Comment: 13 pages, 3 figure

Multiconfiguration Dirac-Hartree-Fock energy levels and transition probabilities for 3d^5 in Fe IV

Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic dipole (M1) transition probabilities are reported for transitions between levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the agreement in the length and velocity forms of the line strength for the E2 transitions are used as indicators of accuracy. The present E2 and M1 transition probabilities are compared with earlier Breit-Pauli results and other theories. An extensive set of transition probabilites with indicators of accuracy are reported in Appendices A and B. Recommended values of A(E2) + A(M1) are listed in Appendix C.Comment: 16 pages, three appendices containing accuracy indicators and recommended values for E2 and M1 transition rate

Beyond density functional theory: the domestication of nonlocal potentials

Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned. This review summarizes motivation for extending current DFT to include nonlocal one-electron potentials, and proposes methodology for implementation of the theory. The theoretical model, orbital functional theory (OFT), is shown to be exact in principle for the general N-electron problem. In practice it must depend on a parametrized correlation energy functional. Functionals are proposed suitable for short-range Coulomb-cusp correlation and for long-range polarization response correlation. A linearized variational cellular method (LVCM) is proposed as a common formalism for molecules and solids. Implementation of nonlocal potentials is reduced to independent calculations for each inequivalent atomic cell.Comment: Accepted for publication in Modern Physics Letters B (2004

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

What catch data can tell us about the status of global fisheries

The only available data set on the catches of global fisheries are the official landings reported annually by the Food and Agriculture Organization of the United Nations (FAO). Attempts to detect and interpret trends in these data have been criticized as being both technically and conceptually flawed. Here, we explore and refute these claims. We show explicitly that trends in catch data are not an artifact of the applied method and are consistent with trends in biomass data of fully assessed stocks. We also show that, while comprehensive stock assessments are the preferred method for evaluating single stocks, they are a biased subsample of the stocks in a given area, strongly underestimating the percentage of collapsed stocks. We concur with a recent assessment-based analysis by FAO that the increasing trends in the percentage of overexploited, depleted, and recovering stocks and the decreasing trends in underexploited and moderately exploited stocks give cause for concern. We show that these trends are much more pronounced if all available data are considered

On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.Comment: (1 figure