Mode-coupling theory for aging in active glasses: relaxation dynamics and evolution towards steady state.
basic_science · Level V
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- Also identified by DOI 10.1039/d6sm00312e.
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Abstract
Aging refers to the evolution of system properties with waiting time <i>t</i><sub>w</sub>. It is a key feature of glassy dynamics. Recent experiments have demonstrated aging in biological systems that are inherently active with a magnitude of self-propulsion force <i>f</i><sub>0</sub> and a persistence time <i>τ</i><sub>p</sub>. Thus, what governs the aging dynamics in these active systems has fundamental importance. We formulate a generic mode-coupling theory (MCT) of active glasses to address this question in the regime when activity is not too large. The aging solutions of the theory show that the two-point correlation function decays more slowly with growing <i>t</i><sub>w</sub>, and the relaxation time <i>t</i><sub>r</sub> increases. The activity-modification of the MCT critical point, <i>λ</i><sub>C</sub>, has profound significance for active aging: the quench distance from <i>λ</i><sub>C</sub> governs aging and determines the aging exponent, <i>δ</i>, where <i>t</i><sub>r</sub> ∼ <i>t</i>δw. <i>δ</i> decreases with increasing <i>f</i><sub>0</sub>, in agreement with existing simulations. However, the variation with <i>τ</i><sub>p</sub> depends on the nature of activity. Our work has fundamental theoretical implications for active glasses and paves the way for a deeper understanding of the aging dynamics in biological systems.