2023/12/07 by Haoran Wang, Wang, Haoran · 1 citation
Mathematics · Physics and Astronomy · #35B65 #42B37 #Analysis of PDEs (math.AP) #FOS: Mathematics #Magnetic properties of thin films #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2312.04002
openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the doubled magnetic Schrödinger operator Hα,B0=(i∇-((B0|x|)/(2)+\fracα|x|)(-(x2)/(|x|),(x1)/(|x|)))2, x=(x1,x2)∈\R2∖\0\, where (B0|x|)/(2)(-(x2)/(|x|),(x1)/(|x|)) stands for the homogeneous magnetic potential with B0>0 and \fracα|x|(-(x2)/(|x|),(x1)/(|x|)) is the well-known Aharonov-Bohm potential with α∈\R∖ℤ. In this note, we obtain an improved time-decay estimate for the Schrödinger flow e^-itHα,B0. The key ingredient is the dispersive estimate for e^-itHα,B0, which was established in \citeWZZ23 recently. This work is motivated by L. Fanelli, G. Grillo and H. Kovař'ık \citeFGK15 dealing with the scaling-critical electromagnetic potentials in two and higher dimensions.