Communication: Pade spectrum decomposition of Fermi function and Bose function

Journal Article · Tue Sep 14 04:00:00 EDT 2010 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3484491· OSTI ID:21559912

Jie, Hu ^[1]; Ruixue, Xu ^[2]; Yijing, Yan ^[1]

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1. Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong)
2. Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)

Pade approximant is exploited for an efficient sum-over-poles decomposition of Fermi and Bose functions. The resulting poles are all pure imaginary and can therefore be used to define Pade frequencies, in analogy with the celebrated Matsubara frequencies. The proposed Pade spectrum decomposition is shown to be equivalent to a truncated continued fraction. It converges significantly faster than other schemes such as the Matsubara expansion at all temperatures. By introducing the characteristic validity length as the measure of approximant, we analyze the convergence properties of different schemes thoroughly. Our results qualify the present scheme the best among all sum-over-poles approaches. Thus, it is of great value in efficient numerical evaluations of integrals involving Fermi/Bose function in various condensed-phase matter problems.

• OSTI ID: 21559912
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 10 Vol. 133; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
CHEMICAL REACTIONS
CONTINUED FRACTIONS
CONVERGENCE
DECOMPOSITION
EVALUATION
EXPANSION
FERMIONS
FUNCTIONS
SPECTRA