对 Peierls-Onsager 替换的全新视角
数学物理
2026-01-26 v1 math.MP
摘要
我们通过强烈局部化紧致帧和磁性矩阵，为有限 Bloch 本征值族在局部谱间隙假设下的通用版本的 Peierls-Onsager 替换进行了表述。这一扩展将结果推广到无需慢变化假设且无需对相关 Bloch 子束进行平凡性假设的长程磁场。此外，我们的结果涵盖了广泛的周期椭圆型伪微分算子。我们还证明了对于初始状态支持于孤立 Bloch 族范围内的情形，存在近似时间演化，且具有精确的误差控制。
引用
@article{arxiv.2601.16745,
title = {A fresh look at the Peierls-Onsager substitution},
author = {Horia D. Cornean and Bernard Helffer and Radu Purice},
journal= {arXiv preprint arXiv:2601.16745},
year = {2026}
}
备注
This paper is a revised version of our preprint "A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields" (arXiv 2411.14171); the main results are the same but the proof strategy has been simplified putting more emphasise on Parseval frames. arXiv admin note: text overlap with arXiv:2411.14171