On calculating the Berry curvature of Bloch electrons using the KKR method

We propose and implement a particularly effective method for calculating the Berry curvature arising from adiabatic evolution of Bloch states in wave vector k space. The method exploits a unique feature of the Korringa-Kohn-Rostoker (KKR) approach to solve the Schr\"odinger or Dirac equations. Namely, it is based on the observation that in the KKR method k enters the calculation via the structure constants which depend only on the geometry of the lattice but not the crystal potential. For both the Abelian and non-Abelian Berry curvature we derive an analytic formula whose evaluation does not require any numerical differentiation with respect to k. We present explicit calculations for Al, Cu, Au, and Pt bulk crystals.Comment: 13 pages, 5 figure

Unnesting of Copatterns

Inductive data such as finite lists and trees can elegantly be defined by constructors which allow programmers to analyze and manipulate finite data via pattern matching. Dually, coinductive data such as streams can be defined by observations such as head and tail and programmers can synthesize infinite data via copattern matching. This leads to a symmetric language where finite and infinite data can be nested. In this paper, we compile nested pattern and copattern matching into a core language which only supports simple non-nested (co)pattern matching. This core language may serve as an intermediate language of a compiler. We show that this translation is conservative, i.e. the multi-step reduction relation in both languages coincides for terms of the original language. Furthermore, we show that the translation preserves strong and weak normalisation: a term of the original language is strongly/weakly normalising in one language if and only if it is so in the other. In the proof we develop more general criteria which guarantee that extensions of abstract reduction systems are conservative and preserve strong or weak normalisation. \ua9 2014 Springer International Publishing Switzerland

First-principles calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas–van Alphen oscillation

POPLMark reloaded: Mechanizing proofs by logical relations

We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks

Topological superconductivity in a phase-controlled Josephson junction

Topological superconductors can support localized Majorana states at their boundaries(1-5). These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner(6,7). Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states(8-21). Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field(22). We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems

First Physics Results at the Physical Pion Mass from Nf=2N_f = 2 Wilson Twisted Mass Fermions at Maximal Twist

We present physics results from simulations of QCD using $N_f = 2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a \approx 0.09$ fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\Delta$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.Comment: 45 pages, 15 figure

The effect of time-to-surgery on outcome in elderly patients with proximal femoral fractures

<p>Abstract</p> <p>Background</p> <p>Whether reducing time-to-surgery for elderly patients suffering from hip fracture results in better outcomes remains subject to controversial debates.</p> <p>Methods</p> <p>As part of a prospective observational study conducted between January 2002 and September 2003 on hip-fracture patients from 268 acute-care hospitals all over Germany, we investigated the relationship of time-to-surgery with frequency of post-operative complications and one-year mortality in elderly patients (age ≥65) with isolated proximal femoral fracture (femoral neck fracture or pertrochanteric femoral fracture). Patients with short (≤12 h), medium (> 12 h to ≤36 h) and long (> 36 h) times-to-surgery, counting from the time of the fracture event, were compared for patient characteristics, operative procedures, post-operative complications and one-year mortality.</p> <p>Results</p> <p>Hospital data were available for 2916 hip-fracture patients (mean age (SD) in years: 82.1 (7.4), median age: 82; 79.7% women). Comparison of groups with short (n = 802), medium (n = 1191) and long (n = 923) time-to-surgery revealed statistically significant differences in a few patient characteristics (age, American Society of Anesthesiologists ratings classification and type of admission) and in operative procedures (total hip endoprosthesis, hemi-endoprosthetic implants, other osteosynthetic procedures). However, comparison of these same groups for frequency of postoperative complications revealed only some non-significant associations with certain complications such as post-operative bleeding requiring treatment (early surgery patients) and urinary tract infections (delayed surgery patients). Both unadjusted rates of one-year all-cause mortality (between 18.1% and 20.5%), and the multivariate-adjusted hazard ratios (HR for time-to-surgery: 1.04; p = 0.55) showed no association between mortality and time-to-surgery.</p> <p>Conclusion</p> <p>Although this study found a trend toward more frequent post-operative complications in the longest time-to-surgery group, there was no effect of time-to-surgery on mortality. Shorter time-to-surgery may be associated with somewhat lower rates of post-operative complications such as decubitus ulcers, urinary tract infections, thromboses, pneumonia and cardiovascular events, and with somewhat higher rates of others such as post-operative bleeding or implant complications.</p