Energy basis via decoherence

The question of the emergence of a preferred basis which is generally under stood as that basis in which the reduced density matrix is driven to a diag onal (classically interpretable) form via environment induced decoherence i s addressed. The exact solutions of the Caldeira-Leggett Master Equation ar e analyzed for a free particle and a harmonic oscillator system. Tn both ca ses, we see that the reduced density matrix is driven diagonal in the energ y basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the p referred basis which is contrary to the general notion that it is the posit ion basis which is selected since the coupling to the environment is via th e position coordinates.