32,028 research outputs found

    Algebra diagrams: a HANDi introduction

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    A diagrammatic notation for algebra is presented – Hierarchical Al- gebra Network Diagrams, HANDi. The notation uses a 2D network notation with systematically designed icons to explicitly and coherently encode the fun- damental concepts of algebra. The structure of the diagrams is described and the rules for making derivations are presented. The key design features of HANDi are discussed and compared with the conventional formula notation in order demonstrate that the new notation is a more logical codification of intro- ductory algebra

    Reciprocity of gauge operators in N=4 SYM

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    A recently discovered generalized Gribov-Lipatov reciprocity holds for the anomalous dimensions of various twist operators in N=4 SYM. Here, we consider a class of scaling psu(2,2|4) operators that reduce at one-loop to twist-3 maximal helicity gluonic operators. We extract from the asymptotic long-range Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections.Comment: Latex, JHEP style, 36 pages, v2: references adde

    Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth Particle Mesh Ewald Method

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    The smooth particle mesh Ewald (SPME) method is the standard method for computing the electrostatic interactions in the molecular simulations. In this work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the accuracy of the SPME method. Unlike the SPME that achieves higher accuracy by refining the mesh, the MSME improves the accuracy by averaging the standard SPME forces computed on, e.g. MM, staggered meshes. We prove, from theoretical perspective, that the MSME is as accurate as the SPME, but uses M2M^2 times less mesh points in a certain parameter range. In the complementary parameter range, the MSME is as accurate as the SPME with twice of the interpolation order. The theoretical conclusions are numerically validated both by a uniform and uncorrelated charge system, and by a three-point-charge water system that is widely used as solvent for the bio-macromolecules

    Dielectric properties of multiband electron systems: I - Tight-binding formulation

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    The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a 2×22\times2 form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations.Comment: 32 pages, LaTeX, to appear in Z.Phys.

    The structure of quotients of the Onsager algebra by closed ideals

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    We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

    Estimate of the Cutoff Errors in the Ewald Summation for Dipolar Systems

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    Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.Comment: 22 pages, 6 figures, Revtex style, submitted to J. Chem. Phy
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