A generalization of Rayleigh's theorem for the infinite harmonic crystal

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Abstract

We show that if one replaces N masses in an infinite harmonic, perfect ν-dimensional crystal by N1 lighter and N2 heavier ones such that N1+ N2 =N is finite, then one introduces at most vN1 (isolated) bound states. This can be considered as an extension of the results of Romerio and Wreszinski.

Original languageEnglish
Pages (from-to)53-58
Number of pages6
JournalJournal of Statistical Physics
Volume18
Issue number1
DOIs
StatePublished - Jan 1978
Externally publishedYes

Keywords

  • impurities
  • isolated frequencies
  • Lattice dynamics

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