We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schrodinger Hamiltonian H generically produces a lack of the classical time-decay for the associated Schrodinger 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

Fanelli, L., Felli, V., Fontelos, M., Primo, A. (2018). Frequency-dependent time decay of Schrödinger flows. JOURNAL OF SPECTRAL THEORY, 8(2), 509-521 [10.4171/JST/204].

Frequency-dependent time decay of Schrödinger flows

Felli, V;
2018

Abstract

We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schrodinger Hamiltonian H generically produces a lack of the classical time-decay for the associated Schrodinger 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
Articolo in rivista - Articolo scientifico
Decay estimates; Electromagnetic potentials; Representation formulas; Schrödinger equation;
Schrödinger equation; electromagnetic potentials; representation formulas; decay estimates.
English
2018
8
2
509
521
open
Fanelli, L., Felli, V., Fontelos, M., Primo, A. (2018). Frequency-dependent time decay of Schrödinger flows. JOURNAL OF SPECTRAL THEORY, 8(2), 509-521 [10.4171/JST/204].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/206215
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