Gumbel distribution and current fluctuations in critical systems

TL;DR

This paper explores a phase transition in current fluctuations of bacteriorhodopsin, revealing that the fluctuations follow a generalized Gumbel distribution near the transition between tunneling regimes, indicating universal behavior under extreme conditions.

Contribution

It demonstrates that current fluctuations during a phase transition in tunneling regimes follow a generalized Gumbel distribution, highlighting a universal pattern in extreme fluctuations.

Findings

Current fluctuations follow a generalized Gumbel distribution near the transition.

The transition occurs around 3 V in the current-voltage characteristics.

Fluctuation behavior is universal under extreme conditions.

Abstract

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.