Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds on the growth of Sobolev norms in some linear time
  dependent Schr\"odinger equations   In this paper we consider linear, time dependent Schr\"odinger 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-Schr\"odinger
equation on the sphere. In each case, $V(t)$ is a smooth and periodic in time
pseudodifferential operator and the Schr\"odinger equation has solutions
fulfilling $\| \psi(t) \|_r \gtrsim |t|^{r }$ as $|t| \gg 1$.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex