9,922 research outputs found

    q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)

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    We study the properties of one-dimensional hypergeometric integral solutions of the q-difference ("quantum") analogue of the Knizhnik-Zamolodchikov-Bernard equations on tori. We show that they also obey a difference KZB heat equation in the modular parameter, give formulae for modular transformations, and prove a completeness result, by showing that the associated Fourier transform is invertible. These results are based on SL(3,Z) transformation properties parallel to those of elliptic gamma functions.Comment: 39 page

    CLUSTEREASY: A Program for Simulating Scalar Field Evolution on Parallel Computers

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    We describe a new, parallel programming version of the scalar field simulation program LATTICEEASY. The new C++ program, CLUSTEREASY, can simulate arbitrary scalar field models on distributed-memory clusters. The speed and memory requirements scale well with the number of processors. As with the serial version of LATTICEEASY, CLUSTEREASY can run simulations in one, two, or three dimensions, with or without expansion of the universe, with customizable parameters and output. The program and its full documentation are available on the LATTICEEASY website at http://www.science.smith.edu/departments/Physics/fstaff/gfelder/latticeeasy/. In this paper we provide a brief overview of what CLUSTEREASY does and the ways in which it does and doesn't differ from the serial version of LATTICEEASY.Comment: 3 pages, 1 figur
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