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PreprintCC BY-NC-SA 4.0arXiv

Universal Long-distance Tail of Particle-number Density near a Wall in Superfluids

  • Keisuke Fujii
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Abstract

We investigate the long-distance recovery of the particle-number density near a static, impermeable wall in a d-dimensional Galilean-invariant superfluid. Using superfluid effective field theory (EFT) on a half-space, we show that quantum phonon fluctuations produce a z−(d+1) tail in the smooth density profile at zero temperature, where z is the distance from the wall. The tail coefficient is fixed by the bulk equation of state and is independent of microscopic wall details. At low temperature T, the thermal length cs/T, with cs the bulk sound speed, separates the zero-temperature behavior at intermediate distances from a thermal Tz−d tail at larger distances for d>1. For d=1, the long-distance phonon contribution instead decays as exp(−4πTz/cs). The EFT applies to both Bose and Fermi superfluids, including strongly interacting Fermi gases at unitarity. We estimate the normalized tail amplitude in three dimensions across the BCS--BEC crossover using experimental sound-speed data.

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Cite

BibTeXRIS
BibTeX
@misc{fujii2026universal,
  title = {{Universal Long-distance Tail of Particle-number Density near a Wall in Superfluids}},
  author = {Keisuke Fujii},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23165},
  eprint = {2610.23165},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23165},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Universal Long-distance Tail of Particle-number Density near a Wall in Superfluids
AU  - Keisuke Fujii
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23165
UR  - https://arxiv.org/abs/2610.23165
AB  - We investigate the long-distance recovery of the particle-number density near a static, impermeable wall in a d-dimensional Galilean-invariant superfluid. Using superfluid effective field theory (EFT) on a half-space, we show that quantum phonon fluctuations produce a z^−(d+1) tail in the smooth density profile at zero temperature, where z is the distance from the wall. The tail coefficient is fixed by the bulk equation of state and is independent of microscopic wall details. At low temperature T, the thermal length c_s/T, with c_s the bulk sound speed, separates the zero-temperature behavior at intermediate distances from a thermal Tz^−d tail at larger distances for d>1. For d=1, the long-distance phonon contribution instead decays as exp(−4πTz/c_s). The EFT applies to both Bose and Fermi superfluids, including strongly interacting Fermi gases at unitarity. We estimate the normalized tail amplitude in three dimensions across the BCS--BEC crossover using experimental sound-speed data.
ER  -