G. C. Levine, M. J. Bantegui, J. A. Burg
The Full Counting Statistics (FCS) is studied for a one-dimensional system of non-interacting fermions with and without disorder. For two $L$ site translationally invariant lattices connected at time $t=0$, the charge variance increases logarithmically in $t$, following the universal expression $<\delta N^2>\approx \frac{1}{\pi^2}\log{t}$, for $t$ much shorter than the ballistic time to encounter the boundary, $t_{b} \sim L$. Since the static charge variance for a length $l$ region is given by $<\delta N^2>\approx \frac{1}{\pi^2}\log{l}$, this result reflects the underlying relativistic or conformal invariance and dynamical exponent $z=1$. With disorder and strongly localized fermions, we have compared our results to a model with a dynamical exponent $z \ne 1$ and also a recently proposed model for entanglement entropy by Igloi, et al, based upon dynamical scaling at the Infinite Disorder Fixed Point (IDFP). The latter scaling, which predicts $<\delta N^2> \propto \log\log{t}$, appears to better describe the FCS of disordered 1-d fermions.
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http://arxiv.org/abs/1201.3933
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