2011/01/31 by Bernhard Baumgartner, Heide Narnhofer · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #quant-ph #msc:81Q99 #msc:60J99 #msc:47S99 #msc:46C99
paper · pdf · doi:10.1142/s0129055x12500018
arxiv created 2011/11/21 · arxiv updated 2015/05/27
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to decay, orthogonal subspaces support the stationary states. Specialities where the complete positivity of evolutions is actually needed for analysis, mainly for evolution of coherence, are highlighted. Decompositions are done the same way for evolutions in discrete as in continuous time, but evolutions may show differences, only for discrete semigroups there may appear cases of sudden decay and of perpetual oscillation. Concluding the analysis we identify the relation of the state space structure to the processes of Decay, Decoherence, Dissipation and Dephasing.