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 TMF, 1991, Volume 86, Number 1, Pages 81–97 (Mi tmf5424)

Topological interaction of phonons with dislocations and disclinations. II. The scattering problem

E. M. Serebryanyi

Abstract: Scattering of acoustic phonons by linear defects is studied in the continuum limit of elasticity theory and the scattering matrix induced by the change in the phase of a phonon that passes round a defect in a closed contour is calculated. It is shown that on the background of a screw dislocation and for negative Frank angle of a disclination phonon modes containing components with kinetic angular momentum $\mu$ satisfying the inequality $0<|\mu|<1$ are singular, namely, near the defect line such components can increase unboundedly as $\rho^\mu$, where $\rho$ is the distance to the line of the defect. In the presence of singular modes, the curvature of the gauge group $G=SO(3)\rhd T(3)$, which is concentrated on the defects, leads to transitions between different polarizations. The topological interaction plays a leading role in the case when the phonon wavelength is much greater than the scattering length corresponding to scattering by the short-range potential of the defect core and, thus, it is most important in problems with long-range correlations.

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English version:
Theoretical and Mathematical Physics, 1991, 86:1, 55–66

Bibliographic databases:

Citation: E. M. Serebryanyi, “Topological interaction of phonons with dislocations and disclinations. II. The scattering problem”, TMF, 86:1 (1991), 81–97; Theoret. and Math. Phys., 86:1 (1991), 55–66

Citation in format AMSBIB
\Bibitem{Ser91} \by E.~M.~Serebryanyi \paper Topological interaction of phonons with dislocations and disclinations. II.~The~scattering problem \jour TMF \yr 1991 \vol 86 \issue 1 \pages 81--97 \mathnet{http://mi.mathnet.ru/tmf5424} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 1 \pages 55--66 \crossref{https://doi.org/10.1007/BF01018497} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GC79000007}