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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Communication: Padé spectrum decomposition of Fermi function and Bose function.

Jie Hu1, Rui-Xue Xu, Yijing Yan

  • 1Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR, China.

The Journal of Chemical Physics
|September 21, 2010
PubMed
Summary

This study introduces a novel Padé approximant method for decomposing Fermi and Bose functions, offering faster convergence than Matsubara expansions for condensed-phase matter calculations.

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Area of Science:

  • Condensed-matter physics
  • Computational physics
  • Quantum mechanics

Background:

  • Fermi and Bose functions are crucial in describing quantum systems.
  • Efficient numerical evaluation of integrals involving these functions is computationally intensive.
  • Existing methods like Matsubara expansion have limitations in convergence and accuracy.

Purpose of the Study:

  • To develop a more efficient sum-over-poles decomposition for Fermi and Bose functions.
  • To introduce Padé frequencies as an alternative to Matsubara frequencies.
  • To analyze and compare the convergence properties of different decomposition schemes.

Main Methods:

  • Exploiting Padé approximants for sum-over-poles decomposition.
  • Defining Padé frequencies from the imaginary poles of the approximant.
  • Analyzing convergence using characteristic validity length.
  • Comparing with Matsubara expansion and other schemes.

Main Results:

  • The Padé spectrum decomposition is equivalent to a truncated continued fraction.
  • Padé frequencies are pure imaginary, analogous to Matsubara frequencies.
  • The proposed scheme shows significantly faster convergence than Matsubara expansion across all temperatures.
  • The Padé approximant method is identified as the superior sum-over-poles approach.

Conclusions:

  • The Padé approximant method provides a highly efficient and accurate approach for sum-over-poles decomposition.
  • This method offers significant advantages for numerical evaluations in condensed-phase matter problems.
  • Padé frequencies represent a valuable tool for analyzing quantum systems.