## Abstract

Randomly distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage above which the current flows in an array of a Coulomb blockade (CB). We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally coupled CB arrays and propose a general relationship between conductance and distribution. In addition, we show that the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different heights. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the CB model but is instructive in statistical physics generally.

Original language | English |
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Article number | 051137 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 84 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 29 2011 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics