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VOLUME 58 | ISSUE 8 | PAGE 636
Distribution of exponential decay rates of localized eigenfunctions in finite quasi 1D disordered systems
For a quasi-ID disordered system of finite length L (a thick wire or a random banded matrix) we found the explicit form of the distribution of the quantity r |V>(0)V>(£)|2, with 1^(0) and xp(L) being the values of an eigenfunction at the opposite ends of the sample. For a long sample the quantity — lnr is shown to have a normal distribution with a variance being twice as large as the mean. The latter determines the smallest Lyapunov exponent (inverse localization length).