  We study the long-time tails of the survival probability $P(t)$ of an $A$
particle diffusing in $d$-dimensional media in the presence of a concentration
$\rho$ of traps $B$ that move sub-diffusively, such that the mean square
displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$.
Starting from a continuous time random walk (CTRW) description of the motion of
the particle and of the traps, we derive lower and upper bounds for $P(t)$ and
show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus
determining asymptotically exact results. The asymptotic decay law in this
regime is exactly that obtained for immobile traps. This means that for
sufficiently subdiffusive traps, the moving $A$ particle sees the traps as
essentially immobile, and Lifshitz or trapping tails remain unchanged. For
$\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide,
leading to a decay law equal to that of a stationary particle. Thus, in this
regime the moving traps see the particle as essentially immobile. For $d>2$,
however, the upper and lower bounds in this $\gamma$ regime no longer coincide
and the decay law for the survival probability of the $A$ particle remains
ambiguous.

Statistical Mechanics