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Einstein-Hopf drag, Doppler shift of thermal radiation and blackbody drag: Three perspectives on quantum friction

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Central European Journal of Physics

Abstract

The thermal friction force acting on an atom moving relative to a thermal photon bath has recently been calculated on the basis of the fluctuation-dissipation theorem. The thermal fluctuations of the electromagnetic field give rise to a drag force on an atom provided one allows for dissipation of the field energy via spontaneous emission. The drag force exists if the atomic polarizability has a nonvanishing imaginary part. Here, we explore alternative derivations. The damping of the motion of a simple harmonic oscillator is described by radiative reaction theory (result of Einstein and Hopf), taking into account the known stochastic fluctuations of the electromagnetic field. Describing the excitations of the atom as an ensemble of damped harmonic oscillators, we identify the previously found expressions as generalizations of the Einstein-Hopf result. In addition, we present a simple explanation for blackbody friction in terms of a Doppler shift of the thermal radiation in the inertial frame of the moving atom: The atom absorbs blue-shifted photons from the front and radiates off energy in all directions, thereby losing energy. The original plus the two alternative derivations provide for additional confirmation of an intriguing quantum friction effect, and leave no doubt regarding its existence.

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Authors and Affiliations

  1. International Institute of Molecular and Cell Biology, Trojdena 4, 02109, Warsaw, Poland

    Grzegorz Łach

  2. Physikalisches Institut der Universität, Albert-Ueberle-Strasse 3-5, 69120, Heidelberg, Germany

    Grzegorz Łach & Maarten DeKieviet

  3. Department of Physics, Missouri University of Science and Technology, Rolla, Missouri, 65409-0640, USA

    Ulrich D. Jentschura

  4. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany

    Ulrich D. Jentschura

Authors
  1. Grzegorz Łach
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  2. Maarten DeKieviet
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  3. Ulrich D. Jentschura
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Correspondence to Ulrich D. Jentschura.

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Łach, G., DeKieviet, M. & Jentschura, U.D. Einstein-Hopf drag, Doppler shift of thermal radiation and blackbody drag: Three perspectives on quantum friction. centr.eur.j.phys. 10, 763–767 (2012). https://doi.org/10.2478/s11534-012-0035-x

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  • DOI: https://doi.org/10.2478/s11534-012-0035-x

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