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  • Open Access

Plasma oscillations within Israel-Stewart theory

L. Gavassino

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England, United Kingdom

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Phys. Rev. D 113, 023035 – Published 20 January, 2026

DOI: https://doi.org/10.1103/b8yz-9rj7

Abstract

It is well known that, at zero wave number, the nonhydrodynamic frequencies of uncharged kinetic theory are purely imaginary. On the other hand, it was recently shown that, in resistive magnetohydrodynamics, the interplay between the Israel-Stewart relaxation equation and the Ampère-Maxwell law can give rise to a pair of oscillating nonhydrodynamic modes. In this work, we analyze this phenomenon in detail. We first demonstrate that these oscillatory modes are exact solutions of the Drude model, corresponding to ordinary plasma oscillations. We then invoke the Onsager-Casimir principle to explain that their oscillatory nature reflects the distinct PT-transformation properties of the degrees of freedom: the distribution function is even, while the electric field is odd. Finally, we establish that, in a kinetic theory of charged particles, there can be at most one such pair of oscillatory modes per spatial dimension, while all other modes still must sit on the imaginary axis.

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Phys. Rev. D 113, 023035– Published 20 January, 2026
  • Received 24 November 2025
  • Accepted 5 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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