  It has been speculated that quantum gravity might induce a "foamy" space-time
structure at small scales, randomly perturbing the propagation phases of
free-streaming particles (such as kaons, neutrons, or neutrinos). Particle
interferometry might then reveal non-standard decoherence effects, in addition
to standard ones (due to, e.g., finite source size and detector resolution.) In
this work we discuss the phenomenology of such non-standard effects in the
propagation of electron neutrinos in the Sun and in the long-baseline reactor
experiment KamLAND, which jointly provide us with the best available probes of
decoherence at neutrino energies E ~ few MeV. In the solar neutrino case, by
means of a perturbative approach, decoherence is shown to modify the standard
(adiabatic) propagation in matter through a calculable damping factor. By
assuming a power-law dependence of decoherence effects in the energy domain
(E^n with n = 0,+/-1,+/-2), theoretical predictions for two-family neutrino
mixing are compared with the data and discussed. We find that neither solar nor
KamLAND data show evidence in favor of non-standard decoherence effects, whose
characteristic parameter gamma_0 can thus be significantly constrained. In the
"Lorentz-invariant" case n=-1, we obtain the upper limit gamma_0<0.78 x 10^-26
GeV at 95% C.L. In the specific case n=-2, the constraints can also be
interpreted as bounds on possible matter density fluctuations in the Sun, which
we improve by a factor of ~ 2 with respect to previous analyses.
