Mass propagation for electromagnetic Schrödinger evolutions. (April 2022)

• Record Type: Journal Article
• Authors: Barceló, Juan Antonio; Cassano, Biagio; Fanelli, Luca
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: 35A23 -- 35J10 -- 35Q41; Schrödinger equation -- Uncertainty principle -- Carleman inequalities -- Magnetic potentials; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112734
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the validity of Gaussian lower bounds for solutions to an electromagnetic Schrödinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a suitable geometric condition is satisfied by the vector potential, then positive masses inside of a bounded region at a single time propagate outside the region, provided a suitable average in space–time cylinders is taken.