  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.
