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We study in some detail the master equation, and its solution in a simplifiedcase modelling flavour oscillations of a two-level system, stemming from theLiouville-string approach to quantum space time foam. In this framework wediscuss the appearance of diffusion terms and decoherence due to theinteraction of low-energy string matter with space-time defects, such asD-particles in the specific model of ``D-particle foam'', as well as darkenergy contributions. We pay particular attention to contrasting the decoherentrole of a cosmological constant in inducing exponential quantum damping in theevolution of low-energy observables, such as the probability of flavouroscillations, with the situation where the dark energy relaxes to zero forasymptotically large times, in which case such a damping is absent. Ourfindings may be of interest to (astrophysical) tests of quantum space-time foammodels in the not-so-distant future.Comment: 27 pages late

Liouville decoherence in a model of flavor oscillations in the presence of dark energy