2013/11/15 by Lloyd P. Sanders, Michael A. Lomholt, Ludvig Lizana +3 · 1 citation
Physics and Astronomy · #physics.chem-ph #cond-mat.stat-mech #physics.bio-ph
paper · pdf · doi:10.1088/1367-2630/16/11/113050
published as New J. Phys. 16 113050 (2014) · 5 pages, 4 figures
arxiv created 2013/11/15 · arxiv updated 2014/12/24
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment. Each particle in this single file is trapped for a random waiting time τ with power law distribution ψ(τ)≃τ-1- α, such that the τ values are independent, local quantities for all particles. From scaling arguments and simulations, we find that for the scale-free waiting time case 0<α<1, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) ⟨ x2(t)⟩≃(log t)1/2. This extreme slowing down compared to regular single file motion ⟨ x2(t)⟩≃ t1/2 is due to the high likelihood that the labeled particle keeps encountering strongly immobilized neighbors. For the case 1<α<2 we observe the MSD scaling ⟨ x2(t)⟩≃ tγ, where γ<1/2, while for α>2 we recover Harris law ≃ t1/2.