Abstract
In a number of recent publications, [1] – [5], we have discussed the asymptotic form of the dynamics of a general type of random one-dimensional chains. The equations we discuss are of the form
are independent positive random variables. Equations of this type arise in a variety of physical contexts. They can represent a master equation for hopping-type transport over random barriers (the Cn=1, the Wn,n+1 random hopping rates); a master equation for excitation transfer along a one-dimensional array of traps of random depth (the Cn random Boltzmann factors, the Wn,n+1=1); an electric transmission line (the Cn random capacitors or the Wn,n+1 random conductances); a random Heisenberg ferromagnetic chain at low temperatures (the Cn=1, Vn representing spin wave destruction operators, and the Wn,n+1 random near-neighbor exchange integrals). Replacing dVn/dt in (1) by d2Vn/dt2, they represent a harmonic chain with random masses (the Cn) or random force constants (the Wn,n+1).
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References
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Alexander, S., Bernasconi, J., Schneider, W.R., Orbach, R. (1981). Excitation Dynamics in Random One-Dimensional Systems. In: Bernasconi, J., Schneider, T. (eds) Physics in One Dimension. Springer Series in Solid-State Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81592-8_32
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DOI: https://doi.org/10.1007/978-3-642-81592-8_32
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