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- W2785118974 abstract "In this paper we consider linear, time dependent Schrodinger equations of the form $i partial_t psi = K_0 psi + V(t) psi $, where $K_0$ is a positive self-adjoint operator with discrete spectrum and whose spectral gaps are asymptotically constant. We give a strategy to construct bounded perturbations $V(t)$ such that the Hamiltonian $K_0 + V(t)$ generates unbounded orbits. We apply our abstract construction to three cases: (i) the Harmonic oscillator on $mathbb R$, (ii) the half-wave equation on $mathbb T$ and (iii) the Dirac-Schrodinger equation on the sphere. In each case, $V(t)$ is a smooth and periodic in time pseudodifferential operator and the Schrodinger equation has solutions fulfilling $| psi(t) |_r gtrsim |t|^{r }$ as $|t| gg 1$." @default.
- W2785118974 created "2018-02-02" @default.
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- W2785118974 date "2018-01-21" @default.
- W2785118974 modified "2023-09-23" @default.
- W2785118974 title "Lower bounds on the growth of Sobolev norms in some linear time dependent Schrodinger equations" @default.
- W2785118974 hasPublicationYear "2018" @default.
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