As far as we can tell, the phi_Q term is not related directly to the spreading of the wave-packet. It arises as a quantum correction to phase factors during periods of free evolution. At this point, we do not have any other physical interpretation. We do not know yet how this term would manifest itself in the other approaches (path-integrals, ABCD theorem and etc.). This remains an interesting topic for future work, but is outside the scope of our article.
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