A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page

Disorder, spin-orbit, and interaction effects in dilute Ga1−xMnxAs{\rm Ga}_{1-x}{\rm Mn}_x{\rm As}

We derive an effective Hamiltonian for ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ in the dilute limit, where ${\rm Ga}_{1-x}{\rm Mn}_x {\rm As}$ can be described in terms of spin $F=3/2$ polarons hopping between the {\rm Mn} sites and coupled to the local {\rm Mn} spins. We determine the parameters of our model from microscopic calculations using both a variational method and an exact diagonalization within the so-called spherical approximation. Our approach treats the extremely large Coulomb interaction in a non-perturbative way, and captures the effects of strong spin-orbit coupling and Mn positional disorder. We study the effective Hamiltonian in a mean field and variational calculation, including the effects of interactions between the holes at both zero and finite temperature. We study the resulting magnetic properties, such as the magnetization and spin disorder manifest in the generically non-collinear magnetic state. We find a well formed impurity band fairly well separated from the valence band up to $x_{\rm active} \lesssim 0.015$ for which finite size scaling studies of the participation ratios indicate a localization transition, even in the presence of strong on-site interactions, where $x_{\rm active}<x_{\rm nom}$ is the fraction of magnetically active Mn. We study the localization transition as a function of hole concentration, Mn positional disorder, and interaction strength between the holes.Comment: 15 pages, 12 figure

Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics

Positional Disorder, Spin-Orbit Coupling and Frustration in GaMnAs

We study the magnetic properties of metallic GaMnAs. We calculate the effective RKKY interaction between Mn spins using several realistic models for the valence band structure of GaAs. We also study the effect of positional disorder of the Mn on the magnetic properties. We find that the interaction between two Mn spins is anisotropic due to spin-orbit coupling within both the so-called spherical approximation and in the more realistic six band model. The spherical approximation strongly overestimates this anistropy, especially for short distances between Mn ions. Using the obtained effective Hamiltonian we carry out Monte Carlo simulations of finite and zero temperature magnetization and find that, due to orientational frustration of the spins, non-collinear states appear in both valence band approximations for disordered, uncorrelated Mn impurities in the small concentration regime. Introducing correlations among the substitutional Mn positions or increasing the Mn concentration leads to an increase in the remnant magnetization at zero temperature and an almost fully polarized ferromagnetic state.Comment: 17 Pages, 13 Figure

High-fidelity simulations of CdTe vapor deposition from a new bond-order potential-based molecular dynamics method

CdTe has been a special semiconductor for constructing the lowest-cost solar cells and the CdTe-based Cd1-xZnxTe alloy has been the leading semiconductor for radiation detection applications. The performance currently achieved for the materials, however, is still far below the theoretical expectations. This is because the property-limiting nanoscale defects that are easily formed during the growth of CdTe crystals are difficult to explore in experiments. Here we demonstrate the capability of a bond order potential-based molecular dynamics method for predicting the crystalline growth of CdTe films during vapor deposition simulations. Such a method may begin to enable defects generated during vapor deposition of CdTe crystals to be accurately explored

IT tools and standards supporting mass customisation in the building industry

Research demonstrate that productivity in the Danish building and construction industry has only doubled over the last fifty years, whereas the manufacturing industry has increased six times. Utilisation of mass customization as a strategy has achieved results in the manufacturing industry in terms of increasing productivity and competitiveness, so the strategy might have potentials in the building and construction industry as well. However, mass customization as a strategy for improving the productivity of the building and construction industry has not been explored as much as in the manufacturing industry. The purpose of this paper is to analyse the assumptions and possibilities for applying the principles of mass customisation related to establishing an adaptable integrated system of entities in the value chain of the building and construction industry. The outset of the paper is a literature review concerning the utilisation of mass customization as a strategy in terms of increasing productivity within the building and construction industry. An essential part of the paper is a case study of 11 building and construction companies and an analysis of the conditions for cooperation between the entities in the value chain of the building and construction industry. The paper induces to which extent it makes sense to talk about utilisation of mass customisation by applying the Industry Foundation Classes (IFC) and standardisation initiatives of the construction industry provided by buildingSMART, and at the same time harvesting the benefits of the mass customization

Suppression of decoherence by bath ordering

The dynamics of two coupled spins-1/2 coupled to a spin-bath is studied as an extended model of the Tessieri-Wilkie Hamiltonian \cite{TWmodel}. The pair of spins served as an open subsystem were prepared in one of the Bell states and the bath consisted of some spins-1/2 is in a thermal equilibrium state from the very beginning. It is found that with the increasing the coupling strength of the bath spins, the bath forms a resonant antiferromagnetic order. The polarization correlation between the two spins of the subsystem and the concurrence are recovered in some extent to the isolated subsystem. This suppression of the subsystem decoherence may be used to control the quantum devices in practical applications.Comment: 32 pages, Chinese Physics (accepted

Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties