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- W2023204204 abstract "As a function of a parameter ensuremath{alpha}, measuring the amount of disorder, we derive asymptotic results (including higher corrections) for the density of eigenstates scrN(E) and the inverse localization length ensuremath{gamma}(E) at frequencies ${ensuremath{omega}}^{2}$=Eensuremath{rightarrow}0 in a harmonic chain with random masses. The same is done for the frequency-dependent diffusion coefficient ${D}^{(0)}$(z) and Burnett coefficient ${D}^{(2)}$(z) as zensuremath{rightarrow}0 in the hopping random barrier (RBM) and random jump rate models (RJM) with static disorder (bond and site problem, respectively). The disorder is described by random jump rates ${w}_{n}$ or random masses ${m}_{n}$=1/${w}_{n}$ with a probability distribution ensuremath{rho}(w)=(1-ensuremath{alpha})${w}^{mathrm{ensuremath{-}}ensuremath{alpha}}$CTHETA(1-w) with ensuremath{alpha}<1. With increasing disorder, i.e., increasing ensuremath{alpha}, the above quantities pass from universal behavior in weakly disordered systems through several regions of nonuniversal behavior. A typical result is the long-time tail of the velocity autocorrelation function in the RBM: with ${ensuremath{delta}}_{0}$=2/(2-ensuremath{alpha}) for 0ensuremath{alpha}1, ${ensuremath{delta}}_{0}$=1-ensuremath{alpha}/2 for -1ensuremath{alpha}0, and ${ensuremath{delta}}_{0}$=(3/2) (universal) for ensuremath{alpha}-1, with crossover behavior ${ensuremath{varphi}}^{(0)}$(t)ensuremath{sim}${t}^{mathrm{ensuremath{-}}1}$ (ln t${)}^{mathrm{ensuremath{-}}2}$ at ensuremath{alpha}=0 and ${ensuremath{varphi}}_{0}$(t)ensuremath{sim}${t}^{mathrm{ensuremath{-}}3/2}$ ln t at ensuremath{alpha}=-1." @default.
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- W2023204204 title "Transport and spectral properties of strongly disordered chains" @default.
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- W2023204204 doi "https://doi.org/10.1103/physrevb.31.3518" @default.
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