Abstract
Quantum vacuum fluctuations of the electromagnetic field in empty space seem not to produce observable effects over the motion of a charged test particle. However, when a change in the background vacuum state is implemented, as for instance when a conducting boundary is introduced, dispersions of the particle velocity may occur. As a consequence, besides the existence of classical effects due to the interaction between particle and boundary, there will be a quantum contribution to the motion of the particle whose magnitude depends on how fast the transition between the different vacuum states occurs. Here this issue is revisited and a smooth transition with a controllable switching time between the vacuum states of the system is implemented. Dispersions of the particle velocity in both, zero and finite temperature regimes are examined. More than just generalizing previous results for specific configurations, new effects are unveiled. Particularly, it is shown that the well known vacuum dominance reported to occur arbitrarily near the wall is a consequence of assumed idealizations. The use of a controllable switching enables us to conclude that thermal effects can be as important as, or even stronger than, vacuum effects arbitrarily near the wall. Additionally, the residual effect predicted to occur in the late time regime was here shown to be linked to the duration of the transition. In this sense, such effect is understood to be a sort of particle energy exchanging due to the vacuum state transition. Furthermore, in certain arrangements a sort of cooling effect over the motion of the particle can occur, i.e., the kinetic energy of the particle is lessen by a certain amount due to subvacuum quantum fluctuations.
Highlights
This issue was further discussed in a toy model based on a real massless scalar field [8], where the contribution to the kinetic energy of the test particle was calculated under certain assumptions
To the classical effects due to the interaction between the charged particle and the wall, a change in its kinetic energy sourced by the switched vacuum state takes place
Regarding the above mentioned subvacuum fluctuations, they consist of phenomena related to the occurrence of negative quantum expectation values of quantities that are positive defined in the realm of classical physics
Summary
We start by summarizing the main aspects about the system we would like to study. Suppose that a non relativistic test particle of mass m and electric charge q, initially in empty space, experiences a smooth transition to a space containing an infinity perfectly conducting flat wall, which is placed at z = 0. Where Fτs,τ (t) is a switching function that allows a smooth transition between the two scenarios above described, and Ej(x, t)Ej(x, t ) vacuum denotes the j-th component of the renormalized electric field correlation function (positive Wightman two-point function). The model exhibiting a sudden transition [1] can be exactly described by setting Fτs,τ (t) → Θ(t)Θ(τ − t), where the unit step function Θ(t) is equal to 0 for t < 0, and 1 for t ≥ 1 In such idealized case the leading contribution for the residual dispersion (τ /z 1) of the particle velocity perpendicular to the wall is given by (∆v⊥)2 ≈ q2/(4π2m2z2), while in the parallel directions (∆v )2 ≈ −q2/(3π2m2τ 2), which vanishes when τ → ∞. I.e., a process that takes an infinite duration, is obtained by setting τs ∼ τ → ∞
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