Global and local relaxation of a spin-chain under exact Schroedinger and   master-equation dynamics
  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. 
Markus J. Henrich (1), Mathias Michel (1), Michael Hartmann (1),   Guenther Mahler (1), Jochen Gemmer (2) ((1) Institute of ...