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Smooth frequency distribution derived from complex phases

A new technique for phonons in polymer chains
  • Christhard Schmid
Conference paper
Part of the Progress in Colloid & Polymer Science book series (PROGCOLLOID, volume 58)

Abstract

The frequency distribution g (ω) (density of states at frequency ω) of an isolated polymer chain (with arbitrary number γ of degrees of freedom per unit cell) is usually calculated approximately as a histogram from the phase frequency curve ω β(φ) (β = 1,..., γ) with a large set of real phases φ). In this paper a method is presented for calculating g (ω) exactly as a rational function of a small set of complex phases φi (ω) (i = 1,…, n 0γ, n 0 - range of interaction). The φi (ω) are the roots of a frequency dependent secular equation the coefficients of which are obtained by the theory of invariants (differentiation of the algorithm of Leverrier-Souriau). The method is of basic importance also for the computation of the Green function in space energy representation for realistic polymers. Analytical results are obtained for a polyatomic linear chain with arbitrary γ and n 0 = 1.

Keywords

Dispersion Relation Polynomial Matrix Complex Phasis Solid State Phys Dynamical Matrix 
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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Copyright information

© Dr. Dietrich Steinkopff Verlag GmbH & Co. KG 1975

Authors and Affiliations

  • Christhard Schmid
    • 1
  1. 1.Institut Laue-LangevinGrenoble

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