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PreprintCC BY 4.0arXiv

Robust Golden Ratio universality as a consequence of a circulant symmetry

  • Luka Paljk
  • Johannes Schmidt
  • Vladislav Popkov
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Abstract

We find a robust scenario for the emergence of the Golden Ratio (GR) dynamical universality class, characterized by the dynamical exponent z ≡ φ=1/2(1+√5). Previously, its emergence required fine-tuning of system parameters. Here, the GR universality class appears generically in a wide class of Markov processes as a consequence of a global, circulant symmetry of the flux Jacobian. This symmetry leads to GR universality in systems where the total number of conservation laws is odd and larger than three. We introduce a multilane exclusion process with Bernoulli stationary measure as a minimal, parameter-free model, which features GR universality for all conserved modes, most of which are doubly degenerate. Our predictions, based on mode-coupling theory generalized to treat degenerate conserved modes, are corroborated by large-scale Monte Carlo simulations.

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Cite

BibTeXRIS
BibTeX
@misc{paljk2026robust,
  title = {{Robust Golden Ratio universality as a consequence of a circulant symmetry}},
  author = {Luka Paljk and Johannes Schmidt and Vladislav Popkov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13842},
  eprint = {2610.13842},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13842},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Robust Golden Ratio universality as a consequence of a circulant symmetry
AU  - Luka Paljk
AU  - Johannes Schmidt
AU  - Vladislav Popkov
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13842
UR  - https://arxiv.org/abs/2610.13842
AB  - We find a robust scenario for the emergence of the Golden Ratio (GR) dynamical universality class, characterized by the dynamical exponent z ≡ φ=1/2(1+√5). Previously, its emergence required fine-tuning of system parameters. Here, the GR universality class appears generically in a wide class of Markov processes as a consequence of a global, circulant symmetry of the flux Jacobian. This symmetry leads to GR universality in systems where the total number of conservation laws is odd and larger than three. We introduce a multilane exclusion process with Bernoulli stationary measure as a minimal, parameter-free model, which features GR universality for all conserved modes, most of which are doubly degenerate. Our predictions, based on mode-coupling theory generalized to treat degenerate conserved modes, are corroborated by large-scale Monte Carlo simulations.
ER  -