Universal time-dependence of the mean-square displacement in extremely rugged energy landscapes with equal minima

Jeppe Dyre, Jacob M. Jacobsen

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    This paper presents a calculation of the time dependence of the mean-square displacement for symmetric random energy barrier hopping models at low temperatures, where the frequency dependence of the normalized diffusion constant D-tilde becomes universal, i.e., independent of the energy barrier probability distribution [J. C. Dyre, Phys. Rev. B 49, 11 709 (1994)]. The universal time dependence of the mean-square displacement is calculated from the effective medium approximation (EMA) universality equation, D-tilde lnD-tilde=s-tilde, where s-tilde is the dimensionless imaginary frequency, as well as for the approximation to the EMA universality equation D-tilde~=s-tilde/ln(1+s-tilde). At long times the universal mean-square displacement is linear in time, corresponding to ordinary diffusion, whereas the mean-square displacement at short times t in dimensionless units varies as 2/ln(t-1).
    TidsskriftPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics)
    Udgave nummer3
    Sider (fra-til)2429-2433
    StatusUdgivet - 1995

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