# Ageing single file motion

Research output: Contribution to journal › Article

### Standard

**Ageing single file motion.** / Metzler, R.; Sanders, Lloyd; Lomholt, M. A.; Lizana, L.; Fogelmark, Karl; Ambjörnsson, Tobias.

Research output: Contribution to journal › Article

### Harvard

*The European Physical Journal. Special Topics*, vol. 223, no. 14, pp. 3287-3293. https://doi.org/10.1140/epjst/e2014-02333-5

### APA

*The European Physical Journal. Special Topics*,

*223*(14), 3287-3293. https://doi.org/10.1140/epjst/e2014-02333-5

### CBE

### MLA

*The European Physical Journal. Special Topics*. 2014, 223(14). 3287-3293. https://doi.org/10.1140/epjst/e2014-02333-5

### Vancouver

### Author

### RIS

TY - JOUR

T1 - Ageing single file motion

AU - Metzler, R.

AU - Sanders, Lloyd

AU - Lomholt, M. A.

AU - Lizana, L.

AU - Fogelmark, Karl

AU - Ambjörnsson, Tobias

PY - 2014

Y1 - 2014

N2 - The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral 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 tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (0) log (1/2)(t) when 0 < alpha < 1. In the intermediate case 1 < alpha < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris' law. Once alpha 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.

AB - The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral 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 tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (0) log (1/2)(t) when 0 < alpha < 1. In the intermediate case 1 < alpha < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris' law. Once alpha 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.

U2 - 10.1140/epjst/e2014-02333-5

DO - 10.1140/epjst/e2014-02333-5

M3 - Article

VL - 223

SP - 3287

EP - 3293

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

SN - 1951-6355

IS - 14

ER -