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First-principles theory of the Casimir screening effect

Yury A. Budkov1,2,3,* and Petr E. Brandyshev1,2

  • 1Laboratory of Computational Physics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia
  • 2School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia
  • 3Laboratory of Multiscale Modeling of Molecular Systems, G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Akademicheskaya st. 1, 153045 Ivanovo, Russia

  • *Contact author: ybudkov@hse.ru
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Phys. Rev. E 111, 044130 – Published 21 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044130

Abstract

In this paper, we use the formalism of finite-temperature quantum field theory to investigate the Casimir force between flat, ideally conductive surfaces containing confined, but mobile ions. We demonstrate that, in the Gaussian approximation, the ionic fluctuations contribute separately from the electromagnetic fluctuations that are responsible for the standard Casimir effect. This is in line with the “separation hypothesis,” which has been previously applied on a purely intuitive basis. Our analysis demonstrates the significance of calculating the zero Matsubara frequency component in the electromagnetic contribution, using the formula developed by Schwinger et al., as opposed to the approach based on Lifshitz theory used by other researchers.

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Phys. Rev. E 111, 044130– Published 21 April, 2025
  • Received 19 November 2024
  • Revised 13 February 2025
  • Accepted 10 April 2025
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