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We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k = 2, over general p-adic rings and even equal characteristic local rings. These can be evaluated by a simple stationary phase estimate when k is not divisible by p, giving an essentially sharp bound for their size. We give a more complicated stationary phase estimate to evaluate them in the case when k is divisible by p. This gives both an upper bound and a lower bound showing the upper bound is essentially sharp. This generalizes previously known bounds in the case of ℤ/p. The lower bounds in the equal characteristic case have two applications to function field number theory, showing that certain short interval sums and certain moments of Dirichlet L-functions do not, as one might hope, admit square-root cancellation.
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This content will become publicly available on August 1, 2026
Thermal phase fluctuations in narrow superfluid rings
We have characterized the effects of thermal phase fluctuations in narrow rings of ultracold Fermi superfluids in the unitary regime and demonstrated that matter-wave interference may be reliably used to measure angular variations in the phase difference between two concentric, coplanar superfluid rings. When one of the rings is cut with a barrier, we find that phase fluctuations around that ring can be large enough to degrade the reliability of protocols for control of quantized circulation states. The effect is greatest when the one-dimensional density is low and the coupling between rings is negligible. In this limit, our measurements are consistent with a correlation length smaller than the system size, as expected from theory. These results establish the crucial role of phase fluctuations for experiments involving ultracold superfluids in elongated circuit-like geometries.
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- Award ID(s):
- 2046097
- PAR ID:
- 10628537
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review A
- Volume:
- 112
- Issue:
- 2
- ISSN:
- 2469-9926
- Page Range / eLocation ID:
- 023314
- Subject(s) / Keyword(s):
- Fermi gases Fermionic condensates Superfluids Ultracold gases Interferometry
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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