کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4964605 | 1447815 | 2016 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential
ترجمه فارسی عنوان
یک روش عددی برای محاسبه مشتقات توابع ماتریسهای بزرگ و کاربرد آن به اپراتور دیراک با همپوشانی در پتانسیل شیمیایی محدود
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
شیمی
شیمی تئوریک و عملی
چکیده انگلیسی
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular with implicit Krylov-Ritz-type approximations. An important use case for the method is the evaluation of the overlap Dirac operator in lattice Quantum Chromodynamics (QCD) at finite chemical potential, which requires the application of the sign function of a non-Hermitian matrix to some source vector. While the sign function of non-Hermitian matrices in practice cannot be efficiently approximated with source-independent polynomials or rational functions, sufficiently good approximating polynomials can still be constructed for each particular source vector. Our method allows for an efficient calculation of the derivatives of such implicit approximations with respect to the gauge field or other external parameters, which is necessary for the calculation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo or Langevin simulations. We also give an explicit deflation prescription for the case when one knows several eigenvalues and eigenvectors of the matrix being the argument of the differentiated function. We test the method for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on realistic SU(3) gauge field configurations on lattices with sizes as large as 14Ã143 and 6Ã183.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 208, November 2016, Pages 135-148
Journal: Computer Physics Communications - Volume 208, November 2016, Pages 135-148
نویسندگان
Matthias Puhr, Pavel Buividovich,