Mathers Systematic Theology - Chapter 2

INSPIRATION OF THE SCRIPTURES 2.1 The Inspiration of the Scriptures involves the accurate recording of the revelation. 2.1.1 Central Passages establish the inspiration of the Scriptures. 2.1.1.1 2 Timothy 3:16-1

The Way Forward: From Sanctions to Supports

The New York City Working Group on School Transformation brought together education practitioners, school reformers, policy-makers, advocates, and parent and student leaders to propose alternatives to the school closings policy of the New York City Department of Education (DOE). (See the list of Working Group members in Appendix 1.) The group was initiated by the New York City Coalition for Educational Justice and coordinated by the Annenberg Institute for School Reform following the fall 2011 conference Effective Alternatives to School Closings: Transforming Struggling Schools in New York City. This report presents the Working Group's conclusions about the limitations of school closings and a set of recommendations for systemic responses to the needs of struggling schools

Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the Swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle and even momentum coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.Comment: 6 pages, 3 figure

Oscillating terms in the Renyi entropy of Fermi liquids

In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and Fermi liquids corresponding to $2k_F$-like oscillations. Our theoretical tools are the one dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface. We compare this term to numerical calculations of entanglement using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find excellent agreement up to moderate interaction strengths.Comment: 8 pages, 2 figure