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.
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