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Abstract
The dynamical systems discussed here are long chains of particles with randomly distributed masses; both nearest- and next-nearest-neighbour harmonic forces are taken into account. It is shown that in order to find the spectrum of frequencies of vibration the distribution of eigenvalues of a large matrix of special type must be determined, and an accurate and rapid method of computing this distribution is described. By this means the vibrational spectra for several degrees of next-nearest-neighbour interactions are found; they are shown to lend support to a theory relating their main features to similar features in the spectra of almost regular chains possessing defect modes.
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Boukahil A, Huber DL. Dynamics of one-dimensional Heisenberg spin glasses in the high-field limit. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:2978-2984. [PMID: 9976540 DOI: 10.1103/physrevb.50.2978] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Hong H, Kopelman R. Coherent potential theory for interacting bands: Phonons and excitons in substitutionally disordered molecular crystals. J Chem Phys 1973. [DOI: 10.1063/1.1679538] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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The computation of lattice frequency distribution functions by means of continued fractions. ACTA ACUST UNITED AC 1968. [DOI: 10.1016/0031-8914(68)90093-1] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Payton DN, Visscher WM. Dynamics of Disordered Harmonic Lattices. I. Normal-Mode Frequency Spectra for Randomly Disordered Isotopic Binary Lattices. ACTA ACUST UNITED AC 1967. [DOI: 10.1103/physrev.154.802] [Citation(s) in RCA: 116] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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