Gumbel distribution and current fluctuations in critical systems

Details Gumbel distribution and current fluctuations in critical systems Gumbel distribution and current fluctuations in critical systems

2012-04-16

arxiv.org/abs/1204.3411v1

Physics

Condensed Matter

Statistical Mechanics

Paper submitted to UPoN 2012 (Unsolved Problems on Noise and Fluctuations)

Scientific paper

We investigate a particular phase transition between two different tunneling regimes, direct and injection (Fowler-Nordheim), experimentally observed in the current-voltage characteristics of the light receptor bacteriorhodopsin (bR). Here, the sharp increase of the current above about 3 V is theoretically interpreted as the cross-over between the direct and injection sequential-tunneling regimes. Theory also predicts a very special behaviour for the associated current fluctuations around steady state. We find the remarkable result that in a large range of bias around the transition between the two tunneling regimes, the probability density functions can be traced back to the generalization of the Gumbel distribution. This non-Gaussian distribution is the universal standard to describe fluctuations under extreme conditions.

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