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Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains

  • Yogeshwar Prasad
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Abstract

For fermions in a slowly varying aperiodic potential with random interactions Vij/|i−j|α, the potential fixes the resonance supply N0 ∝ L2−n/h. On crossing α−2n, wherever Hartree fragmentation is operative, the resonant-object ensemble reconstructs: turning-point runs fragment into clusters whose intrinsic matching law resolves no logarithmic singularity, while isolated wing bonds survive at finite density and restore a reduced logarithm. The scaling x4−2n−αpair lnxpair ∝ h2/(V t0) is unchanged. Random coefficient fluctuations sustain the R−α coupling; uniform ones cancel to R−α−2.

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Cite

BibTeXRIS
BibTeX
@misc{prasad2026hartree,
  title = {{Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains}},
  author = {Yogeshwar Prasad},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30746},
  eprint = {2608.30746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30746},
}
RIS
TY  - UNPB
TI  - Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains
AU  - Yogeshwar Prasad
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30746
UR  - https://arxiv.org/abs/2608.30746
AB  - For fermions in a slowly varying aperiodic potential with random interactions V_ij/|i−j|^α, the potential fixes the resonance supply N_0 ∝ L^2−n/h. On crossing α−2n, wherever Hartree fragmentation is operative, the resonant-object ensemble reconstructs: turning-point runs fragment into clusters whose intrinsic matching law resolves no logarithmic singularity, while isolated wing bonds survive at finite density and restore a reduced logarithm. The scaling x^4−2n−α_pair lnx_pair ∝ h^2/(V t0) is unchanged. Random coefficient fluctuations sustain the R^−α coupling; uniform ones cancel to R^−α−2.
ER  -