"The numerical accuracy of truncated Ewald sums for periodic systems with long-range Coulomb interactions"

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in the Ewald formulation. We derive an optimal choice for the Fourier-space cutoff given a screening parameter $\eta$. We find that the number of vectors in Fourier space required to achieve a given accuracy scales with $\eta^3$. The proposed method can be used to determine computationally efficient parameters for Ewald sums, to assess the quality of Ewald-sum implementations, and to compare different implementations.Comment: 6 pages, 3 figures (Encapsulated PostScript), LaTe

Topological invariants from non-restricted quantum groups

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this case we show that these invariants are equal and extend to what we call a relative Homotopy Quantum Field Theory which is a branch of the Topological Quantum Field Theory founded by E. Witten and M. Atiyah. Our main examples of relative spherical categories are the categories of finite dimensional weight modules over non-restricted quantum groups considered by C. De Concini, V. Kac, C. Procesi, N. Reshetikhin and M. Rosso. These categories are not semi-simple and have an infinite number of non-isomorphic irreducible modules all having vanishing quantum dimensions. We also show that these categories have associated ribbon categories which gives rise to re-normalized link invariants. In the case of sl(2) these link invariants are the Alexander-type multivariable invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.Comment: 37 pages, 16 figure

Learning in sender-receiver games

game theory;learning;testing

Multiple jumps and vacancy diffusion in a face-centered cubic metal

The diffusion of monovacancies in gold has been studied by computer simulation. Multiple jumps have been found to play a central role in the atomic dynamics at high temperature, and have been shown to be responsible for an upward curvature in the Arrhenius plot of the diffusion coefficient. Appropriate saddle points on the potential energy surface have been found, supporting the interpretation of vacancy multiple jumps as distinct migration mechanisms.Comment: 16 page

Molecular Clouds as the Origin of the Fermi Gamma-Ray GeV-Excess

The so-called "GeV-excess" of the diffuse Galactic gamma-ray emission is studied with a spectral template fit based on energy spectra. The spectral templates can be obtained in a data-driven way from the gamma-ray data, which avoids the use of emissivity models to subtract the standardbackground processes from the data. Instead, one can determine these backgrounds simultaneously with any "signals" in any sky direction, including the Galactic disk and the Galactic center. Using the spectral template fit two hypothesis of the "GeV-excess" were tested: the dark matter (DM) hypothesis assuming the excess is caused by DM annihilation and the molecular cloud (MC) hypothesis assuming the "GeV-excess" is related to a depletion of gamma-rays below 2 GeV, as is directly observed in the Central Molecular Zone (CMZ). Both hypotheses provide acceptable fits, if one considers a limited field-of-view centered within 20$^\circ$ around the Galactic center and applies cuts on the energy range and/or excludes low latitudes, cuts typically applied by the proponents of the DM hypothesis. However, if one considers the whole gamma-ray sky and includes gamma-ray energies up to 100 GeV we find that the MC hypothesis is preferred over the DM hypothesis for several reasons: i) The MC hypothesis provides significantly better fits; ii) The morphology of the "GeV-excess" follows the morphology of the CO-maps, a tracer of MCs, i.e. there exists a strong "GeV-excess" in the Galactic disk also at large longitudes; iii) The massive CMZ with a rectangular field-of-view of $l \times b = 3.5^{\circ} \times 0.5^{\circ}$ shows the maximum of the energy flux per log bin in the diffuse gamma-ray spectrum at 2 GeV, i.e. the "GeV-excess", already in the raw data without any analysis. The rectangular profile contradicts the spherical morphology expected for DM annihilation.Comment: 53 pages, 8 figures (+ 42 figures in Appendices), extended version of arXiv:1610.08926 accepted for publication in PR

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

We report first-principles phase diagram calculations for the binary systems HfC–TiC, TiC–ZrC, and HfC–ZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC–ZrC and HfC–TiC, with consolute temperatures in excess of 2000 K. The HfC–ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ~7%, ~20%, and ~0%, for HfC–TiC, TiC–ZrC, and HfC–ZrC, respectively. Predicted miscibility gaps are symmetric for HfC–ZrC, almost symmetric for HfC–TiC and asymmetric for TiC–ZrC

Broken Time Translation Symmetry as a model for Quantum State Reduction

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born's rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.Comment: 15 pages, 5 figure