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PreprintarXiv licencearXiv

Non-negative differential mobility of one-dimensional underdamped Langevin dynamics: Proof via mapping to a marginally stable oscillator

  • Udo Seifert
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Abstract

For an underdamped particle driven by a constant non-conservative force across a periodic potential in one spatial dimension at finite temperature, numerical studies have shown that the differential mobility is non-negative. Here, an analytical proof will be given that is based on expressing the differential mobility by the long-time mean position of a marginally stable harmonic oscillator subject to noise in its stiffness.

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Cite

BibTeXRIS
BibTeX
@misc{seifert2026nonnegative,
  title = {{Non-negative differential mobility of one-dimensional underdamped Langevin dynamics: Proof via mapping to a marginally stable oscillator}},
  author = {Udo Seifert},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21833},
  eprint = {2609.21833},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21833},
}
RIS
TY  - UNPB
TI  - Non-negative differential mobility of one-dimensional underdamped Langevin dynamics: Proof via mapping to a marginally stable oscillator
AU  - Udo Seifert
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21833
UR  - https://arxiv.org/abs/2609.21833
AB  - For an underdamped particle driven by a constant non-conservative force across a periodic potential in one spatial dimension at finite temperature, numerical studies have shown that the differential mobility is non-negative. Here, an analytical proof will be given that is based on expressing the differential mobility by the long-time mean position of a marginally stable harmonic oscillator subject to noise in its stiffness.
ER  -