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ENERGY DYNAMICS IN A ONE-DIMENSIONAL APERIODIC ANHARMONIC LATTICE

C. A. A. DOS SANTOS

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió - AL, Brazil

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T. F. ASSUNÇÃO

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió - AL, Brazil

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M. L. LYRA

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió - AL, Brazil

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, and

F. A. B. F. DE MOURA

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió - AL, Brazil

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https://doi.org/10.1142/S0129183112400098Cited by:4 (Source: Crossref)

Abstract

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ n^ν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

Keywords:

PACS: 78.30.Ly, 71.30.+h, 73.20.Jc

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