We will discuss recent results on dynamical localization
for a simple, disordered many-body system: the xy-spin chain.
For the model, with a disordered transversal magnetic field, we prove
dynamical localization. This is expressed in terms of a
zero-velocity Lieb-Robinson bound which holds on (disorder) average.
This is joint work with Gunter Stolz (from the University of Alabama at
Birmingham) and Eman Hamza (from Cairo University in Egypt).