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Register a new userProperties of normal modes in a modified disordered Klein-Gordon lattice: From disorder to order
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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 nearest-neighbor interactions. We fix $W=4$ and investigate how the properties of the systems normal modes change as we approach its ordered version, i.e. $Drightarrow 0$. We show that the probability density distribution of the normal modes frequencies takes a `U-shaped profile as $D$ decreases. Furthermore, we use two quantities for estimating the modes spatial extent, the so-called localization volume $V$ (which is related to the modes second moment) and the modes participation number $P$. We show that both quantities scale as $propto D^{-2}$ when $D$ approaches zero and we numerically verify a proportionality relation between them as $V/P approx 2.6$.
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