Quantum vacuum fluctuations near a partially reflecting boundary: Brownian motion of a test charge as probe

The modified vacuum fluctuations of quantum fields in the presence of a perfectly reflecting mirror lead to divergent velocity dispersions of a charged test particle. Here, it is shown that when the mirror is modeled by a material medium described by a Drude-like susceptibility, these dispersions become regular, thus elucidating that the origin of the divergences that appear in the previous treatments is related to the assumption of idealized boundary conditions. As a consequence of implementing this more realistic description, the dispersion curves acquire an oscillatory behavior caused by the effective mass of the field modes inside the dispersive medium. Additionally, it is found that the effects over the particle are delayed when compared to the perfect mirror limit, a phenomenon attributed to the imperfect reflection of field modes on the mirror. Therefore, although idealized boundary conditions are simplifying hypotheses, their usage might hide or significantly modify relevant physical phenomena.

Automated summary

The velocity dispersions of a charged test particle due to modified vacuum fluctuations of quantum fields are divergent under idealized boundary conditions. When the mirror is modeled by a Drude-like susceptibility, these dispersions become regular, indicating that the assumption of idealized boundary conditions is the cause of the divergences. The implementation of a more realistic description reveals that the dispersion curves exhibit oscillatory behavior due to the effective mass of field modes inside the medium.