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Energy diffusion in a pinned harmonic chain with free boundary condition and interactions of increasing range

  • Yipeng Lu
  • Wei Wang
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Abstract

We consider a finite two-dimensional pinned harmonic chain with an interaction range that diverges with the system size and with conservative rotational noise. Under a joint scaling in which the interaction range diverges microscopically but vanishes macroscopically, we prove that the expected em- pirical energy measures converge to the unique measure-valued weak solution of the heat equation.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026energy,
  title = {{Energy diffusion in a pinned harmonic chain with free boundary condition and interactions of increasing range}},
  author = {Yipeng Lu and Wei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08138},
  eprint = {2609.08138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08138},
}
RIS
TY  - UNPB
TI  - Energy diffusion in a pinned harmonic chain with free boundary condition and interactions of increasing range
AU  - Yipeng Lu
AU  - Wei Wang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08138
UR  - https://arxiv.org/abs/2609.08138
AB  - We consider a finite two-dimensional pinned harmonic chain with an interaction range that diverges with the system size and with conservative rotational noise. Under a joint scaling in which the interaction range diverges microscopically but vanishes macroscopically, we prove that the expected em- pirical energy measures converge to the unique measure-valued weak solution of the heat equation.
ER  -