2015/10/13 by L. Fanelli, Luca Fanelli, V. Felli +9
Mathematics · Physics and Astronomy · #35J10 #35L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #math.SP #msc:35J10 #msc:35L05
paper · pdf · doi:10.48550/arxiv.1510.03660
10 pages
arxiv created 2015/10/13 · openalex publication_date 2015/10/13 · arxiv updated 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schrödinger hamiltonian H generically produces a lack of the classical time-decay for the associated Schrödinger flow e-itH. This is in contrast with the fact that dispersive estimates (Strichartz) still hold, in general, also in this case. We also observe an improvement of the decay for higher positive modes, showing that the time decay of the solution is due to the first nonzero term in the expansion of the initial datum as a series of eigenfunctions of a quantum harmonic oscillator with a singular potential. A completely analogous phenomenon is shown for the heat semigroup, as expected.