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PreprintarXiv licencearXiv

Derivation of the Thiele equation for magnetic skyrmions using the Mori-Zwanzig formalism

  • Michael te Vrugt
  • Mathias Kläui
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Abstract

We use the Mori-Zwanzig formalism to derive an exact generalized Langevin equation governing the dynamics of magnetic skyrmions. Using standard approximations, this generalized Langevin equation is found to reduce to the usual Thiele equation. Our approach provides a general route for obtaining extensions of the Thiele equation applicable to magnetic textures and degrees of freedom not covered by the standard derivation route. It also provides some insights into the microscopic justification of the standard Thiele equation, specifically concerning contributions of fast modes to the form of the drift and diffusion terms in the Fokker-Planck equation for skyrmions.

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Cite

BibTeXRIS
BibTeX
@misc{vrugt2026derivation,
  title = {{Derivation of the Thiele equation for magnetic skyrmions using the Mori-Zwanzig formalism}},
  author = {Michael te Vrugt and Mathias Kläui},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24160},
  eprint = {2609.24160},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24160},
}
RIS
TY  - UNPB
TI  - Derivation of the Thiele equation for magnetic skyrmions using the Mori-Zwanzig formalism
AU  - Michael te Vrugt
AU  - Mathias Kläui
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24160
UR  - https://arxiv.org/abs/2609.24160
AB  - We use the Mori-Zwanzig formalism to derive an exact generalized Langevin equation governing the dynamics of magnetic skyrmions. Using standard approximations, this generalized Langevin equation is found to reduce to the usual Thiele equation. Our approach provides a general route for obtaining extensions of the Thiele equation applicable to magnetic textures and degrees of freedom not covered by the standard derivation route. It also provides some insights into the microscopic justification of the standard Thiele equation, specifically concerning contributions of fast modes to the form of the drift and diffusion terms in the Fokker-Planck equation for skyrmions.
ER  -