Quantum Brownian motion near a point-like reflecting boundary

Abstract

The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity and position of the particle are explicitly derived and their behaviors examined. The results are similar to those corresponding to an electric charge interacting with a quantum electromagnetic field near a reflecting plane boundary, mainly regarding the divergent behavior of the dispersions at the origin (where the boundary is placed), and at the time interval corresponding to a round trip of a light pulse between the particle and the boundary.We close by addressing some effects of allowing the position of the particle to fluctuate.

Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle

“…Panel b on the other hand, exhibits negative dispersions in some interval of time. Negative dispersion has also been reported in previous works with both original [17] and modified [18,29,30] system and has been often intrepreted as a consequence of the renormalization with respect to the Minkowski vacuum fluctuations. In Sec.…”

“…1 also illustrate the different behavior in this limit for small time and signs of the dispersions in x and y (or z) directions in this limit. Equations (29) and (30) along with these panels show the absolute values of mean squared velocity fluctuation tends distinctively to zero. The nontrivial topology plays different role even for small time in compact and noncompact directions.…”

Quantum Brownian motion in an analog Friedmann-Robertson-Walker geometry

“…This factor has the same role of a switching sampling function which regularizes these type of integrals (see Refs. [5,6] for this same discussion in flat spacetime).…”

“…[1,2], in flat spacetime such motion appears when one or more reflecting boundaries are present. In this scenario a nonzero mean squared velocity, that depends on the boundary position is found in the transverse and parallel directions to the boundary [3][4][5][6]. Furthermore, some singularities appears in the mean squared velocity even when the usual renormalization techniques, with respect to the Minkowski background, are implemented [3,4].…”

“…One of these singularities is due to the boundaries and the other correspond to the duration of a round trip of the signal between the particle position and the boundary location. Although, as was noted in [5,6], they can be regularized when a switching process is considered and a non-instantaneous interaction between the particle and the field is given.…”