We present the results obtained on the magnetisation relaxation
properties of the XX and Ising quantum chains in a transverse magnetic
field. We first consider an initial thermal kink-like state where half
of the chain is initially thermalized at a very high temperature $T_b$
while the remaining half, called the system, is put at a lower
temperature $T_s$. In this case the front dynamic is studied. We
derive analytically the Green function associated to the dynamical
behaviour of the transverse magnetisation. Depending on the strength
of the magnetic field and on the temperature of the system, different
regimes are obtained for the magnetic relaxation. In particular, with
an initial cold subsystem of finite size in contact at both ends with
an infinite temperature environnement, we derive analytically the
behaviour of the time-dependent system magnetisation. |