  The second quantization of a real massless scalar field in the presence of a
material medium described by a Drude-like susceptibility is here examined in a
1+1 dimensional model. The modified vacuum fluctuations of this field imprint
divergence-free velocity dispersions on a scalar-charged particle, thus
elucidating that the origin of divergences that appear in previous treatments
is the assumption of idealized boundary conditions. Among the findings there is
an oscillation on the dispersion curves caused by the effective mass of the
field modes inside the dispersive medium. Additionally, it is found that the
effects of the medium on the particle are delayed when compared to the perfect
mirror limit, a phenomenon attributed to the imperfect reflection of field
modes on the mirror. Although the study focus on a scalar field, the findings
are valuable for understanding models based on electromagnetic interaction.
