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Vacuum induced dispersions on the motion of test particles in $D+1$ dimensions

When the vacuum state of a scalar or electromagnetic field is modified by the presence of a reflecting boundary, an interacting test particle undergoes velocity fluctuations. Such effect is regarded as a sort of quantum analog of the classical Brownian motion. Several aspects about this system have been recently investigated in the literature, for instance, finite temperature effects, curved spacetime framework, near-boundary regime, late time behavior, and subvacuum phenomena. Here, further steps are given in this analysis by considering the effect of vacuum fluctuations of a scalar field in the presence of a perfectly reflecting flat boundary over the motion of a scalar test particle when the background field does not satisfy the Huygens' principle. Specifically, the background field is allowed to have mass and the system is studied in $D+1$ dimensions. A method of implementing a smooth transition between distinct states of the field is also developed, rendering regularized analytic expressions describing the velocity fluctuations of the test particle. This method is applied to study some special behaviors of the system. Possible applications include fields known to occur in nature as, for instance, the massive Higgs' field, for which the velocity fluctuations are here predicted to acquire a characteristic oscillation, thus behaving differently from their electromagnetic counterparts.