Anti-GZK effect in ultra-high-energy cosmic ray diffusive propagation

We discuss the anti-GZK effect in the diffusive propagation of ultra-high-energy protons in intergalactic magnetic fields, which consists of a jump-like increase of the maximum distance from which ultra-high-energy protons can reach an observer. The position of this jump, E-j ≈ 2 X 10(18) eV, is determined exclusively by energy losses (transition from adiabatic to pair-production energy losses), and it is independent of the diffusion parameters. The diffuse spectrum presents a low-energy steepening approximately at this energy, which is very close to the position of the second knee observed in the cosmic ray spectrum. The dip, seen in the universal spectrum as a signature of the interaction with the cosmic microwave background radiation, is also present in the case of diffusive propagation in magnetic fields.