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PreprintCC BY 4.0arXiv

Level ordering in the linear E ⊗ e dynamic Jahn-Teller model

  • Naoya Iwahara
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Abstract

The ground level of the linear E⊗ e dynamic Jahn-Teller model has long been believed to be the doublet with vibronic angular momentum j = ±1/2. We prove that, for arbitrary coupling strength, the nth level Enj in the subspace of fixed j strictly increases with |j| for every n, En,1/2 < En,3/2 < En,5/2 < ⋯; in particular, the ground level is always the j = ±1/2 doublet. The proof uses only a unitary transformation that lowers j by one, combined with the variational principle. We also show that the levels with fixed j are nondegenerate and give explicit lower and upper bounds on the gap E0,j+1 − E0j. The same Hamiltonian describes Rashba-coupled particles in harmonic traps and, in nuclear physics, the static nucleon in a charged scalar meson field.

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Cite

BibTeXRIS
BibTeX
@misc{iwahara2026level,
  title = {{Level ordering in the linear $E \otimes e$ dynamic Jahn-Teller model}},
  author = {Naoya Iwahara},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38190},
  eprint = {2610.38190},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38190},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Level ordering in the linear E ⊗ e dynamic Jahn-Teller model
AU  - Naoya Iwahara
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38190
UR  - https://arxiv.org/abs/2610.38190
AB  - The ground level of the linear E⊗ e dynamic Jahn-Teller model has long been believed to be the doublet with vibronic angular momentum j = ±1/2. We prove that, for arbitrary coupling strength, the nth level E_nj in the subspace of fixed j strictly increases with |j| for every n, E_n,1/2 < E_n,3/2 < E_n,5/2 < ⋯; in particular, the ground level is always the j = ±1/2 doublet. The proof uses only a unitary transformation that lowers j by one, combined with the variational principle. We also show that the levels with fixed j are nondegenerate and give explicit lower and upper bounds on the gap E_0,j+1 − E_0j. The same Hamiltonian describes Rashba-coupled particles in harmonic traps and, in nuclear physics, the static nucleon in a charged scalar meson field.
ER  -