Neutrino Decoherence from Generalised Uncertainty

Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised uncertainty principle which leads to a modified Heisenberg algebra. This can alter the usual von-Neumann evolution of density matrix to a Lindblad-type equation. We show how this can give rise to a decoherence in neutrino propagation in vacuum. The decoherence effects due to the linear quadratic generalised uncertainty principle are extremely minimal and is unlikely to be detectable in the existing or upcoming experimental facilities for any of the natural sources of neutrinos. We also show that, in principle, there can be other variants of generalised uncertainty principle which predicts verifiable decoherence effects for the cosmic neutrino background.