Ageing memory and glassiness of a driven vortex system

Many systems in nature-glasses, interfaces and fractures being some examples-cannot equilibrate with their environment, which gives rise to novel and surprising behaviour such as memory effects, ageing and nonlinear dynamics. Unlike their equilibrated counterparts, the dynamics of out-of-equilibrium systems is generally too complex to be captured by simple macroscopic laws. Here we investigate a system that straddles the boundary between glass and crystal: a Bragg glass, formed by vortices in a superconductor. We find that the response to an applied force evolves according to a stretched exponential, with the exponent reflecting the deviation from equilibrium. After the force is removed, the system ages with time and its subsequent response time scales linearly with its 'age' (simple ageing), meaning that older systems are slower than younger ones. We show that simple ageing can occur naturally in the presence of sufficient quenched disorder. Moreover, the hierarchical distribution of timescales, arising when chunks of loose vortices cannot move before trapped ones become dislodged, leads to a stretched-exponential response.