Nonlinear Phenomena in Complex Systems, 2020, Vol.23, No.2, pp.165

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2020, Vol.23, No.2, pp.165 - 171

Properties of Normal Modes in a Modified Disordered Klein-Gordon Lattice: From Disorder to Order
B. Senyange, J.-J. du Plessis, B. Many Manda, and Ch. Skokos

We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: D, which determines the range of the coefficients of the on-site potentials, and W, which defines the strength of the nearestneighbor interactions. We fix W = 4 and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. D → 0. We show that the probability density distribution of the normal mode's frequencies takes a 'U'-shaped profile as D decreases. Furthermore, we use two quantities for estimating the mode's spatial extent, the so-called localization volume V (which is related to the mode's second moment) and the mode's participation number P. We show that both quantities scale as ∝ D⁻² when D approaches zero and we numerically verify a proportionality relation between them as V/P ≈ 2.6.

Key words: Klein-Gordon lattice model,localization, normal modes

DOI: https://doi.org/10.33581/1561-4085-2020-23-2-165-171

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