Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid

@misc{le2026surface,
  title = {{Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid}},
  author = {Bao-Duy Le},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24565},
  eprint = {2610.24565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24565},
}

TY  - UNPB
TI  - Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid
AU  - Bao-Duy Le
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24565
UR  - https://arxiv.org/abs/2610.24565
AB  - We study a spin-balanced unitary Fermi superfluid bound by an attractive 1/r interaction within an extended Thomas--Fermi density functional. Its large-particle-number limit is the Lane--Emden polytrope of index 3/2. We prove the leading gradient correction to the ground-state energy and strong convergence of the density amplitude. A rescaled surface problem predicts the next energy correction and the leading integrated density error. Matching a vortex core to the polytropic bulk gives the energetic threshold of a singly quantized central vortex, including the constant beyond the leading logarithm. Linearizing the same surface problem predicts a local energetic threshold for collective surface excitations that, in the natural TF frequency units, decreases more slowly with particle number than the central-vortex threshold. Radial stationary, spherical Bogoliubov--Poisson, and axisymmetric real-time calculations test the predicted energy corrections and vortex matching, and resolve finite-size surface-mode minima whose approach to the continuum surface coefficient is followed to N≃4×10^6. For the reference gradient coefficient the vortex constant is c_1=−0.535, and the surface Landau scale is 1.417 ω_K(ℏ_eff^2/2R_TF)^1/6∝ N^−1/9; sector energies at N≃4.6×10^5, computed after the fit, agree with the extrapolated vortex threshold to 10^−4. These results distinguish the accuracy of the Thomas--Fermi bulk from the gradient physics that controls the surface and vortex core, and separate vortex energetics from the open problem of nonlinear vortex entry.
ER  -