Geodesic
Intersection of phonon spectrum branches
Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 1, pp. 123-126 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the phonon spectrum of a simple crystal lattice as a whole. Topological methods show that, the quasilongitudlnal branch, which is isolated at long wavelengths, must intersect one of the other branches of the spectrum at sufficiently short wavelengths. 
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     author = {V. K. Tkachenko},
     title = {Intersection of phonon spectrum branches},
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V. K. Tkachenko. Intersection of phonon spectrum branches. Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 1, pp. 123-126. http://geodesic.mathdoc.fr/item/TMF_1972_10_1_a10/

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