Search results for "Linear combination"
showing 10 items of 132 documents
Matter Dependence of the Four-Loop Cusp Anomalous Dimension
2019
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals w…
Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six
2017
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.
Relations for Einstein–Yang–Mills amplitudes from the CHY representation
2017
We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with $r$ gravitons and $(n-r)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons. We present a general formula for this case.
Feynman integrals and iterated integrals of modular forms
2017
In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $\varepsilon$ . We discuss explicitly the equal mass sunrise integral and the kite integral. For both cases we give the alphabet of letters occurring in the iterated integrals. For the sunrise integral we present a compact formula, expressing this integral to all orders in $\varepsilon$ as iterated integrals of modular forms.
Computation of form factors in massless QCD with finite master integrals
2016
We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $\epsilon$ expansions and thereby reproduce all known results with an independent method. Remarkably, in our finite basis, only integrals with a less-than-maximal number of propagators contribute to the cusp anomalous dimensions. We report on indications of this phenomenon at four loops, including the result for a finite, irreducible, twelve-propagator form factor integral. Together with this article, we provide our automated software setup for the computation of finite master integrals.
Local structure of perovskites ReO3and ScF3with negative thermal expansion: interpretation beyond the quasiharmonic approximation
2016
We propose an approach beyond the quasiharmonic approximation for interpretation of EXAFS and XRD data and for ab initio calculations of electronic and vibration properties of materials with negative thermal expansion. Ab initio electronic structure and lattice dynamics calculations for cubic and distorted ScF3 were performed using the linear combination of atomic orbitals (LCAO) method. The band gap obtained in calculations for ScF3 is equal to 10.54 eV and agree well with the expected value. The calculated infrared spectra of F displaced (FD) cubic ScF3 allow us to predict that its mean Sc-F-Sc angle within NTE deviates from 180 degree.
Transition levels of acceptor impurities in ZnO crystals by DFT-LCAO calculations
2018
This research was partly supported by the Kazakhstan Science Project № AP05134367«Synthesis of nanocrystals in track templates of SiO2/Si for sensory, nano-and optoelectronic applications» and Latvian Super Cluster (LASC), installed in the Institute of Solid State Physics (ISSP) of the University of Latvia. Authors are indebted to D. Gryaznov, A. Popov and A. Dauletbekova for stimulating discussions.
Atomic and electronic structure of hydrogen on ZnO (11̄00) surface: ab initio hybrid calculations
2013
Hydrogen atoms unavoidably incorporated into ZnO during growth of bulk samples and thin films considerably affect their electrical conductivity. The results of first principles hybrid LCAO calculations are discussed for hydrogen atoms in the bulk and on the non-polar ZnO (100) surface. The incorporation energy, the atomic relaxation, the electronic density redistribution and the electronic structure modifications are compared for the surface adsorption and bulk interstitial H positions. It is shown that hydrogen has a strong binding with the surface O ions (2.7 eV) whereas its incorporation into bulk is energetically unfavorable. Surface hydrogen atoms are very shallow donors, thus, contrib…
An ab initio study of the unimolecular decomposition mechanism of formamidine. 4-31G Characterization of potential energy hypersurface
1991
Ab initio MO calculations have been carried out for the unimolecular decomposition of formamidine. The Hartree–Fock method in LCAO approximation with the 4-31G basis set was used. The 4-31G potential hypersurface has been further studied. The stationary points (R, TS, and P) were localized. A reaction analysis by correlation of bond-order indices and localized molecular orbitals demonstrated that the decomposition is an asynchronous process. The TS can be described as four-membered ring.
Generating harmonic surfaces for interactive design
2014
Abstract A method is given for generating harmonic tensor product Bezier surfaces and the explicit expression of each point in the control net is provided as a linear combination of prescribed boundary control points. The matrix of scalar coefficients of these combinations works like a mould for harmonic surfaces. Thus, real-time manipulation of the resulting surfaces subject to modification of prescribed information is possible.