Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

@misc{jeon2026irrationality,
  title = {{Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems}},
  author = {Junmo Jeon and Shiro Sakai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10948},
  eprint = {2609.10948},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10948},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems
AU  - Junmo Jeon
AU  - Shiro Sakai
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.10948
UR  - https://arxiv.org/abs/2609.10948
AB  - Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.
ER  -