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Exactly solvable models provide an opportunity to study different aspects ofreduced quantum dynamics in detail. We consider the reduced dynamics of asingle spin in finite XX and XY spin 1/2 chains. First we introduce a generalexpression describing the evolution of the reduced density matrix. Thisexpression proves to be tractable when the combined closed system (i.e. opensystem plus environment) is integrable. Then we focus on comparing decoherenceand thermalization timescales in the XX chain. We find that for a single spinthese timescales are comparable, in contrast to what should be expected for amacroscopic body. This indicates that the process of quantum relaxation of asystem with few accessible states can not be separated in two distinct stages -decoherence and thermalization. Finally, we turn to finite-size effects in thetime evolution of a single spin in the XY chain. We observe three consecutivestages of the evolution: regular evolution, partial revivals, irregular(apparently chaotic) evolution. The duration of the regular stage isproportional to the number of spins in the chain. We observe a "quiet and coldperiod" in the end of the regular stage, which breaks up abruptly at somethreshold time.

Entanglement, decoherence and thermal relaxation in exactly solvable models