Recent numerical simulations have shown that the distribution of conductanceP(g) in 3D strongly localized regiem differs significally from the expected lognormal distribution. To understand the origin of this difference analytically,we used a generalized DMPK equation for the joint probablity distribution ofthe transmission eigenvalues which includes a phenomenological (disorder anddimensionality dependent) matrix K containing certain correlations of thetransfer matrices. We first of all examine the assumptions made in thederivation if the generalized DMPK and find that to a good approximation theyremain valid in 3D. We then evaluate the matrix K numerically for variousstrength of the disorder and various system sizes. In the strong disorder limitwe find that K can be described by a simple model which, for a cubic system,depends on a single parameter. We use this phenomenological model toanalytically evaluate the full distribution P(g) for Anderson insulators in 3D.The analytic results allow us to develop an intuitive understanding of theentire distribution, which differs qualitatively from the log-normaldistribution of a Q1D wire. We also show that out method could be applicable inthe critical regime of the Anderson transition.
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