  We study numerically the intraband exciton relaxation in a one-dimensional
lattice with scale-free disorder, in the presence of a linear bias. Exciton
transport is considered as incoherent hoppings over the eigenstates of the
static lattice. The site potential of the unbiased lattice is
long-range-correlated with a power-law spectral density $S(k) \sim
1/k^{\alpha}$, $\alpha > 0$. The lattice supports a phase of extended states at
the center of the band, provided $\alpha$ is larger than a critical value
$\alpha_c$ [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. \textbf{81},
3735 (1998)]. When the bias is applied, the absorption spectrum displays clear
signatures of the Wannier-Stark ladder [E. D\'{\i}az \emph{et al.}, Phys. Rev.
B\textbf{73}, 172410 (2006)]. We demonstrate that in unbiased lattices and in
weakly correlated potentials the decay law is non-exponential. However, the
decay is purely exponential when the bias increases and $\alpha$ is large. We
relate this exponential decay to the occurrence of the Wannier-Stark ladder in
the exciton band.
