Ground States of Nonlinear Fermionic Systems: From Power-Law Interactions to Logarithmic Sobolev Inequality

@misc{chen2026ground,
  title = {{Ground States of Nonlinear Fermionic Systems: From Power-Law Interactions to Logarithmic Sobolev Inequality}},
  author = {Bin Chen and Yujin Guo and Yong Luo and Zhenya Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14568},
  eprint = {2609.14568},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14568},
}

TY  - UNPB
TI  - Ground States of Nonlinear Fermionic Systems: From Power-Law Interactions to Logarithmic Sobolev Inequality
AU  - Bin Chen
AU  - Yujin Guo
AU  - Yong Luo
AU  - Zhenya Yan
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14568
UR  - https://arxiv.org/abs/2609.14568
AB  - We consider ground states of a two-component logarithmic fermionic system in ℝ^d, where d≥ 1 is arbitrary. We prove that up to translations and scalings, ground states of the logarithmic system are the $L^\infty $-limits of ground states for a two-component 2p−1 power-law fermionic system as psearrow 1. As a byproduct, we also establish a sharp logarithmic Sobolev inequality for orthonormal functions in ℝ^d, whose optimizers are, up to scalings, the minimizers of a constraint variational problem associated with the logarithmic system.
ER  -