The Fermi-Dirac (FD) and Bose-Einstein (BE) integrals were applied to a quantum system to estimate the density of particles and relaxation time in some magnetic alloys at low temperatures. An integral part in the ener...The Fermi-Dirac (FD) and Bose-Einstein (BE) integrals were applied to a quantum system to estimate the density of particles and relaxation time in some magnetic alloys at low temperatures. An integral part in the energy equations of vibrations (phonons), spin waves (magnons), and electrons was mathematically treated. Comparison between theoretical and experimental results gave good semi-empirical relations and some physical constants.展开更多
An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma funct...An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.展开更多
In this paper, we present a simple and practical method to compute Fermi-Dirac integrals and modified Fermi-Dirac integrals. Moreover, we apply this method to compute the parameters A⊥^α and A⊥^β in [5] and we get...In this paper, we present a simple and practical method to compute Fermi-Dirac integrals and modified Fermi-Dirac integrals. Moreover, we apply this method to compute the parameters A⊥^α and A⊥^β in [5] and we get the desired result. The parameters are relevant to the dense plasma transport and are very important to the magnet confined plasma dynamics.展开更多
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the mu...Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.展开更多
文摘The Fermi-Dirac (FD) and Bose-Einstein (BE) integrals were applied to a quantum system to estimate the density of particles and relaxation time in some magnetic alloys at low temperatures. An integral part in the energy equations of vibrations (phonons), spin waves (magnons), and electrons was mathematically treated. Comparison between theoretical and experimental results gave good semi-empirical relations and some physical constants.
文摘An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.
文摘In this paper, we present a simple and practical method to compute Fermi-Dirac integrals and modified Fermi-Dirac integrals. Moreover, we apply this method to compute the parameters A⊥^α and A⊥^β in [5] and we get the desired result. The parameters are relevant to the dense plasma transport and are very important to the magnet confined plasma dynamics.
基金supported by the Department of Energy (No.DE-FG02-03ER25587)the Office of Naval Research(No.N00014-01-1-0674)an Alfred P.Sloan Research Fellowship and a startup grant from University of Texas at Austin
文摘Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.
