  We solve the Schroedinger equation for an interacting spin-chain locally
coupled to a quantum environment with a specific degeneracy structure. The
reduced dynamics of the whole spin-chain as well as of single spins is
analyzed. We show, that the total spin-chain relaxes to a thermal equilibrium
state independently of the internal interaction strength. In contrast, the
asymptotic states of each individual spin are thermal for weak but non-thermal
for stronger spin-spin coupling. The transition between both scenarios is found
for couplings of the order of $0.1 \times \Delta E$, with $\Delta E$ denoting
the Zeeman-splitting. We compare these results with a master equation
treatment; when time averaged, both approaches lead to the same asymptotic
state and finally with analytical results.
