Probing quantum vacuum fluctuations over a charged particle near a reflecting wall

We investigate the influence of the vacuum fluctuations of a background electric field over a charged test particle in the presence of a perfectly reflecting flat wall. A switching function connecting different stages of the system is implemented in such a way that its functional dependence is determined by the ratio between the measuring time and the switching duration. The dispersions of the velocity components of the particle are found to be smooth functions of time, and have maximum magnitudes for a measuring time corresponding to about one round trip of a light signal between the particle and the wall. Typical divergences reported in the literature and linked with an oversimplification in modeling this system are naturally regularized in our approach. Estimates suggest that this sort of manifestation of quantum vacuum fluctuations over the motion of the particle could be tested in laboratories.

Figure 1

Quantum dispersion of the parallel components of the particle velocity as a function of time.

Figure 2

Quantum dispersion of the perpendicular component of the particle velocity as a function of time.

Figure 3

Smooth curves given by Eq. (6) (with a dislocated origin) in contrast with the Heaviside-like behavior, represented by the background rectangle.

Figure 4

Dispersion of the parallel components of the particle velocity as a function of $\tau$ for several values of the parameter $n$. Notice that the dispersion becomes negative after $\tau =2z$.

Figure 5

Dispersion of the component of the particle velocity perpendicular to the wall as a function of $\tau$ for several values of the parameter $n$. Notice that the maximum effect occurs just about $\tau =2z$.

Figure 6

Layout (out of scale) of a possible experiment designed to measure the dispersions of the particle velocity induced by vacuum fluctuations. The particle is emitted by a source in the $x$ direction, has its motion influenced by the modified quantum vacuum fluctuations in the wall region, and is measured on a condensation plate.

Figure 7

Distribution of the roots of the polynomial $1+u^{2n}$ in the complex plane. Notice that there are $n$ roots in each half-plane. Here we have used the shorthand notation ${\psi }_{n,p}\equiv {\psi }_p$.