Vibration Frequency Spectra of Disordered Lattices. I. Moments of the Spectra for Disordered Linear Chains

C. Domb; A. A. Maradudin; E. W. Montroll; G. H. Weiss

doi:10.1103/PhysRev.115.18

Vibration Frequency Spectra of Disordered Lattices. I. Moments of the Spectra for Disordered Linear Chains

C. Domb, A. A. Maradudin, E. W. Montroll, and G. H. Weiss

Phys. Rev. 115, 18 – Published 1 July 1959

Abstract

By using the theory of random walks on lattices, a combinatorial expression has been obtained for the even moments of the vibrational frequency spectrum of a randomly disordered, two-component, isotopic linear chain as functions of the concentrations of the two kinds of particles and of their mass ratio. Expressions for the even moments up to $μ_{20}$ are presented.

Received 19 January 1959

DOI:https://doi.org/10.1103/PhysRev.115.18

Authors & Affiliations

C. Domb^* and A. A. Maradudin

Physics Department, University of Maryland, College Park, Maryland

E. W. Montroll and G. H. Weiss

Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland

^*On leave from Physics Department, King's College, University of London.

Vibration Frequency Spectra of Disordered Lattices. II. Spectra of Disordered One-Dimensional Lattices

C. Domb, A. A. Maradudin, E. W. Montroll, and G. H. Weiss

Phys. Rev. 115, 24 (1959)

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Vol. 115, Iss. 1 — July 1959

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