## Abstract

The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling 〈x
^{2}(t)〉 ≃ K
_{1/2}t
^{1/2} as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times τ with a power-law distribution ψ(τ) ≃ (τ
^{★})
^{α}, and different ranges of the exponent α are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris’ law to an ultraslow, logarithmic time evolution 〈x
^{2}(t)〉 ≃ K
_{0} log
^{1/2}(t) when 0 < α < 1. In the intermediate case 1 < α < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris’ law. Once α is larger than two, the Brownian single file behaviour and thus Harris’ law are restored. We also point out that this process is weakly non-ergodic in the sense that the time and ensemble averaged mean squared displacements are disparate.

Original language | English |
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Journal | The European Physical Journal Special Topics |

Volume | 223 |

Issue number | 14 |

Pages (from-to) | 3287-3293 |

ISSN | 1951-6355 |

DOIs | |

Publication status | Published - 2014 |