Disorder correlated

With this work an effort has been made to relate and reduce a wide range of facts and features to a closely specified one-electron band scheme, accommodating as fas as possible the demands made by correlation, disorder, etc. Although much of the basic material has been extensively discussed for some time, it is hoped that the subject does with this paper become further clarified and consolidated. 

Figure 101 Calculated Poole-Frenkel plots according to the correlated disorder model for different values of o jkT (from top curve downward). The calculations according to the Gaussian disorder model with

This distribution appears whenever g a) is given by a power law in (j, coming from the power law variation of the density of linear cracks g l) with their length 1. In the random percolation model considered here, this does not normally occur (except at the percolation threshold p = Pc)- However, for various correlated disorder models, applicable to realistic disorders in rocks, composite materials, etc., one can have such power law distribution for clusters, which may give rise to a Weibull distribution for their fracture strength. We will discuss such cases later, and concentrate on the random percolation model in this section. 

Figure 40. Mobility (/i, plotted as In//) vs. field strength ( , plotted on a scale proportional to as predicted by the Correlated Disorder Model for DOS of various r.m.s. widths a. The disorder is assumed to arise purely from random charge-dipole interactions. The lattice parameter is a. For a = lOA and = 0.1 eV, eaEja = 1 corresponds to a field strength of 10 V cm. (Reprinted with permission from Ref [63f].)...

Mott, N.F., Electrons in disordered structures. Advances in Physics, 1967. 16 p. 49 Moura, F.A.B.F. and M.L. Lyra, Delocalization in the ID Anderson model with long-range correlated disorder. Physical Review Letters, 1998. 81 p. 3735... 

The recent experimental confirmation of the existence of one-dimensional metallic systems has led to a rapid increase in the experimental and theoretical study of these conducting systems. The objective of this section is to acquaint the reader with the physical basis of the concepts currently being used to explain the experimental results. Emphasis is given to the development of one electron band theory because of its central importance in the description of metals and understanding the effects of lattice distortion (Peierls transition), electron correlation, disorder potentials, and interruptions in the strands. It... 

In [221] the X-ray diffraction patterns of PE fibers in the high-pressure hexagonal form have been modeled assuming complete translational disorder along z, rotational disorder of chains around their axes and conformational disorder. The Fourier transforms of disordered structural models were calculated as a function of intra- and inter-molecular parameters related to the presence of conformational disorder and the relative arrangement of close neighboring chains (short-range correlation disorder). The results of the calculations were compared to experimental X-ray diffraction data. 

Applying the replica method in order to average the free energy over different configurations of quenched disorder one finds the effective Hamiltonian of the m-vector model with long-range-correlated disorder [65] ... 

We are interested in the polymer limit m — 0 of the model (28) interpreting it as a model for SAWs in disordered media. Note, that such a limit is not trivial, as explained in the last section. In Refs. [71,72] the asymptotic behavior of SAWs in long-range-correlated disorder of type (25) is investigated and found to be governed by a set of critical exponents which are different from that of the pure case. 

In ref. [48] an environment of a quenched configuration of a semi-dilute polymer solution is introduced as a special case of long-range correlated disorder for polymer dynamics. For the statics this environment is shown to be equivalent to an annealed one, i.e. without impact. 

In the case of long-range-correlated disorder we have another global parameter a along with d, and for the renormalization of the coupling Wo in Eq. (28) one imposes [67] ... 

The effective Hamiltonian (29) is the starting point for a study of the polymer limit m 0 of the weakly diluted Stanley model with long-range-correlated disorder. Imposing the renormalization conditions of the massive scheme in the one-loop approximation leads to the following expressions for the RG functions [72] ... 

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