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The High-Frequency Behaviour of Response Functions

  • Wilhelm Brenig

Abstract

The behaviour of response functions Xkl (z) and Φ kl (z) at high frequencies z can be most easily obtained from the spectral representation (6.5), i.e.
$${\Phi _{kl}}(z)\, = \,\frac{1}{\pi }\,\int_{ - \infty }^{ + \infty } {\frac{{\Phi _{kl}^{ll}(w)}}{{w - z}}} \,dw$$
(11.1)
by a power expansion in descending powers of z. This leads to a series
$${\Phi _{kl}}\left( z \right) = - \frac{1}{\pi }\sum\limits_{n = 0}^\infty {\frac{{\Phi _{kl}^{\left( n \right)}}}{{{z^n}}}.}$$
(11.2)

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Additional Reading

  1. Forster, D.: Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (W.A. Benjamin, Reading, MA 1975) Sect. 2.9Google Scholar
  2. Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II, Springer Ser. Solid-State Sci, Vol.31 (Springer, Berlin, Heidelberg 1985) Sect. 3.7 Mori, H.: Prog. Theor. Phys. 33, 423 (1965)CrossRefGoogle Scholar
  3. Mori, H.: Prog. Theor. Phys. 33, 423 (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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