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A lower bound for two-interval quantum backflow

Primarily AI-generated textHuman understanding: no partsmath.MP — Mathematical Physics

Contributed by Daniel Adam Pyle ↗

Version 1 / Oct 18, 2026 / CC BY 4.0

Abstract

An explicit compactly supported positive-momentum state yields a summed backflow greater than 0.06190 over two unit-duration intervals separated by a gap of 3/2, in units where the reduced Planck constant is 1 and the mass is 1/2. An executable numerical certificate encloses its value approximately between 0.0619551065 and 0.0619551266, conditional on stated arithmetic and library assumptions. The state is defined by stored binary-rational coefficients and is re-integrated with enclosed quadrature and rounding errors. This is a trial-state lower bound, not an optimality result. It exceeds a published conjectural numerical range for equal spacing, but does not establish superiority to the true equal-spacing supremum or publication priority.

Provenance statement

I initiated this project, requested verification, and reviewed the write-up. Lyra, an AI assistant powered by OpenAI, performed the literature search, mathematical calculations, code development, computational checks, audits, and writing. I am an independent researcher without specialist credentials in this subject. The audits and verification runs were also AI-conducted; no outside human specialist has reviewed the mathematics or implementation. Tools included Python, NumPy, SciPy, mpmath interval arithmetic, GCC, MPFR, and a custom FFT implementation with explicit error bounds. The exact underlying AI model version is not established in this submission. This is not official OpenAI research or an OpenAI endorsement. Novelty remains unconfirmed.

Tools used

OpenAI
Lyra — OpenAI AI assistant

References

  1. C. J. Fewster and H. Kirk-Karakaya, Repeated quantum backflow and overflow , Proceedings of the Royal Society A 481 (2025), 20250577. https://doi.org/10.1098/rspa.2025.0577.DOI
  2. H. Kirk-Karakaya, The Quantum Backflow Phenomenon , thesis (2026), Table 3.5. https://etheses.whiterose.ac.uk/id/eprint/38105/8/Kirk-Karakaya_203026398_CorrectedThesisClean2.pdf.link
  3. H. Kirk-Karakaya, Repeated quantum backflow and quantum overflow , original spectral data and programs. https://github.com/hkk506/Repeated-quantum-backflow-and-quantum-overflow/.link

Version history

  1. v1Submitted by Daniel Adam PyleInitial depositCurrentOct 18, 2026