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The Calculation of Brillouin Zone Integrals by Interpolation Techniques

  • R. L. Jacobs
  • D. Lipton
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

In this paper we present a quasi-analytic technique for calculating Brillouin zone integrals of the form
$$\operatorname{Re} {\chi _o}\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{q} ,\omega } \right) = {N^{ - 1}}P\sum\limits_k {{{\left( {f\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} } \right) - f\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{q} } \right)} \right)} \mathord{\left/{\vphantom {{\left( {f\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} } \right) - f\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{q} } \right)} \right)} {\left( {{\varepsilon _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} }} - {\varepsilon _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{q} }} + h\omega } \right).}}} \right. \kern-\nulldelimiterspace} {\left( {{\varepsilon _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} }} - {\varepsilon _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{q} }} + h\omega } \right).}}}$$
(1)

Keywords

Magnetic Susceptibility Energy Band Imperial College Susceptibility Function Interpolation Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Gilat, G. and Haubenheimer, L.J., Phys. Rev., 144, 390 (1966).CrossRefGoogle Scholar
  2. 2.
    Lipton, D. and Jacobs, R.L., J.Phys.C., [2] 3 June (1970).Google Scholar
  3. 3.
    Lipton, D. and Jacobs, R.L., J.Phys.C., to be published.Google Scholar
  4. 4.
    Callaway, J., Phys. Rev., 170. 576 (1968).CrossRefGoogle Scholar
  5. 5.
    Miiler, A.P. and Brockhouse, B.N., Phys. Rev. Letts, 20, 798 (1968).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • R. L. Jacobs
    • 1
  • D. Lipton
    • 1
  1. 1.Mathematics DepartmentImperial CollegeLondonEngland

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