Remarks on the influence of quantum vacuum fluctuations over a charged test particle near a conducting wall

  • V. A. De LorenciEmail author
  • C. C. H. Ribeiro
Open Access
Regular Article - Theoretical Physics


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.


Boundary Quantum Field Theory Thermal Field Theory Stochastic Processes 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    H. Yu and L.H. Ford, Vacuum fluctuations and Brownian motion of a charged test particle near a reflecting boundary, Phys. Rev. D 70 (2004) 065009 [quant-ph/0406122].
  2. [2]
    L.H. Ford, Stochastic spacetime and Brownian motion of test particles, Int. J. Theor. Phys. 44 (2005) 1753 [gr-qc/0501081] [INSPIRE].
  3. [3]
    H. Yu and J. Chen, Brownian motion of a charged test particle in vacuum between two conducting plates, Phys. Rev. D 70 (2004) 125006 [quant-ph/0412010] [INSPIRE].
  4. [4]
    H. Yu, J. Chen and P. Wu, Brownian motion of a charged test particle near a reflecting boundary at finite temperature, JHEP 02 (2006) 058 [hep-th/0602195] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Seriu and C.H. Wu, Switching effect on the quantum Brownian motion near a reflecting boundary, Phys. Rev. A 77 (2008) 022107 [arXiv:0711.2203].ADSCrossRefGoogle Scholar
  6. [6]
    M. Seriu and C.H. Wu, Smearing effect due to the spread of a probe-particle on the Brownian motion near a perfectly reflecting boundary, Phys. Rev. A 80 (2009) 052101 [arXiv:0906.5142] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    V.A. De Lorenci, C.C.H. Ribeiro and M.M. Silva, Probing quantum vacuum fluctuations over a charged particle near a reflecting wall, Phys. Rev. D 94 (2016) 105017 [arXiv:1606.09134] [INSPIRE].ADSGoogle Scholar
  8. [8]
    G.H.S. Camargo et al., Vacuum fluctuations of a scalar field near a reflecting boundary and their effects on the motion of a test particle, JHEP 07 (2018) 173 [arXiv:1709.10392] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    C.H.G. Bessa, V.A. De Lorenci and L.H. Ford, An analog model for light propagation in semiclassical gravity, Phys. Rev. D 90 (2014) 024036 [arXiv:1402.6285] [INSPIRE].ADSGoogle Scholar
  10. [10]
    V.A. De Lorenci and L.H. Ford, Subvacuum effects on light propagation, Phys. Rev. A 99 (2019) 023852 [arXiv:1804.10132] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    V. Sopova and L.H. Ford, The energy density in the Casimir effect, Phys. Rev. D 66 (2002) 045026 [quant-ph/0204125] [INSPIRE].
  12. [12]
    V. Sopova and L.H. Ford, The electromagnetic field stress tensor between dielectric half-spaces, Phys. Rev. D 72 (2005) 033001 [quant-ph/0504143] [INSPIRE].
  13. [13]
    L.H. Ford, Quantum coherence effects and the second law of thermodynamics, Proc. Roy. Soc. A 364 (1978) 227.ADSCrossRefGoogle Scholar
  14. [14]
    L.H. Ford, Constraints on negative energy fluxes, Phys. Rev. D 43 (1991) 3972 [INSPIRE].ADSGoogle Scholar
  15. [15]
    L.H. Ford and T.A. Roman, Restrictions on negative energy density in flat space-time, Phys. Rev. D 55 (1997) 2082 [gr-qc/9607003] [INSPIRE].
  16. [16]
    E.E. Flanagan, Quantum inequalities in two-dimensional Minkowski space-time, Phys. Rev. D 56 (1997) 4922 [gr-qc/9706006] [INSPIRE].
  17. [17]
    C.J. Fewster and S.P. Eveson, Bounds on negative energy densities in flat space-time, Phys. Rev. D 58 (1998) 084010 [gr-qc/9805024] [INSPIRE].
  18. [18]
    C.H.G. Bessa, V.A. De Lorenci, L.H. Ford and C.C.H. Ribeiro, Model for lightcone fluctuations due to stress tensor fluctuations, Phys. Rev. D 93 (2016) 064067 [arXiv:1602.03857] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    L.S. Brown and G.J. Maclay, Vacuum stress between conducting plates: An Image solution, Phys. Rev. 184 (1969) 1272 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N.D. Birrel and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982).CrossRefGoogle Scholar
  21. [21]
    V.A. De Lorenci, E.S. Moreira Jr. and M.M. Silva, Quantum Brownian motion near a point-like reflecting boundary, Phys. Rev. D 90 (2014) 027702 [arXiv:1404.3115] [INSPIRE].ADSGoogle Scholar
  22. [22]
    N. Bartolo et al., Vacuum Casimir energy densities and field divergences at boundaries, J. Phys. Condens. Matter 27 (2015) 214015 [arXiv:1410.1492] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, 7th edition, Academic Press, New York U.S.A. (2007).Google Scholar
  24. [24]
    V.S. Adamchik, Polygamma functions of negative order, J. Comp. Appl. Math. 100 (1998) 191.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Física e QuímicaUniversidade Federal de ItajubáItajubáBrazil
  2. 2.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrazil

Personalised recommendations