Constraints on the spatial variation of Planck constant: Is Earth motion acting on atoms as a field?

Inspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of h ̄ upon the position. The protocols, both within today state of art, involve the use of two delayed laser pulses driving an atom. The distinct positions of the laboratory, due to the Earth motion, affects h ̄ and hence the atomic dynamics. The first protocol measures the difference in population of the atomic ground state while the second one the red-shift of the harmonics emitted by the atom in the two moments of the experiment. The protocols improve the reported upper limit of Δh ̄ /h ̄ . The theory shows that h ̄(r) induces a chaotic evolution to the atom. This form of Chaos is generated by a variation of a physical parameter and is one example of Parametric Chaos.