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PreprintCC BY 4.0arXiv

The electromagnetic stress tensor in cubic crystals and amorphous solids

  • Richard Dengler
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Abstract

The electromagnetic vacuum stress tensor in a system consisting of classical point-like atoms on a cubic lattice is derived directly from the electric field and, alternatively, using the known more phenomenological formula involving the (usually unknown) derivative of the dielectric tensor. The results agree. The stress tensor contains a nontrivial constant and therefore cannot be obtained from macroscopic electrodynamics alone. A system consisting of a mosaic of randomly oriented grains of a cubic crystal is used as a model of an amorphous solid. The electromagnetic stress tensor in this system is deduced by averaging the corresponding quantity in a cubic crystal over all orientations. Two components remain: the component in the direction of the electric field and the component perpendicular to it. The transverse component agrees with the analogous quantity for liquids derived by Peierls in an entirely different way.

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Cite

BibTeXRIS
BibTeX
@misc{dengler2026electromagnetic,
  title = {{The electromagnetic stress tensor in cubic crystals and amorphous solids}},
  author = {Richard Dengler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05969},
  eprint = {2609.05969},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05969},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The electromagnetic stress tensor in cubic crystals and amorphous solids
AU  - Richard Dengler
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05969
UR  - https://arxiv.org/abs/2609.05969
AB  - The electromagnetic vacuum stress tensor in a system consisting of classical point-like atoms on a cubic lattice is derived directly from the electric field and, alternatively, using the known more phenomenological formula involving the (usually unknown) derivative of the dielectric tensor. The results agree. The stress tensor contains a nontrivial constant and therefore cannot be obtained from macroscopic electrodynamics alone. A system consisting of a mosaic of randomly oriented grains of a cubic crystal is used as a model of an amorphous solid. The electromagnetic stress tensor in this system is deduced by averaging the corresponding quantity in a cubic crystal over all orientations. Two components remain: the component in the direction of the electric field and the component perpendicular to it. The transverse component agrees with the analogous quantity for liquids derived by Peierls in an entirely different way.
ER  -