2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/29646We investigate the motion of a domain wall in the presence of a dynamical hyperfine field. At temperature T high compared to the hyperfine coupling, the nuclear spins create a spatially random potential landscape, with dynamics dictated by the nuclear relaxation time $T_2$. The distribution of the domain wall relaxation times (both in the thermal and quantum regimes) can show a long tail, characteristic of stochastic processes where rare events are important. Here, these are due to occasional strong fluctuations in the nuclear spin polarisation.6 pages, LatexMesoscale and Nanoscale Physicstext