Frequency-dependent time decay of Schrödinger flows (Q1650228)

The authors study the classical time-decay properties of the Schrödinger flow generalized by electromagnetic Schrödinger Hamiltonians. Firstly, they show that the presence of negative eigenvalues can destroy the time-decay for the corresponding Schrödinger flow. Secondly, they improve the decay for higher positive modes when the classical time-decay holds. The proof relies on the spectral analysis of the quantum harmonic oscillator.