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Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schr\"odinger Operators

Mathematical Physics 2025-09-05 v1 math.MP Spectral Theory

Abstract

We investigate periodic Schr\"odinger operators in arbitrary dimensions in the large coupling regime. Our results establish that both the Lieb--Robinson velocity and the asymptotic velocity decay at an inverse polynomial rate in the coupling, with the precise exponent determined by the period of the underlying potential. In particular, we obtain sharp polynomial decay rates that capture the precise dependence on the periodic structure.

Keywords

Cite

@article{arxiv.2509.04381,
  title  = {Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schr\"odinger Operators},
  author = {Houssam Abdul-Rahman and Jake Fillman and Christoph Fischbacher and Wencai Liu},
  journal= {arXiv preprint arXiv:2509.04381},
  year   = {2025}
}

Comments

16 pages

R2 v1 2026-07-01T05:21:32.934Z