Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic
  Perturbation: Reducibility and Growth of Sobolev Norms   For a family of 1-d quantum harmonic oscillator with a perturbation which is
$C^2$ parametrized by $E\in{\mathcal I}\subset{\Bbb R}$ and quadratic on $x$
and $-{\rm i}\partial_x$ with coefficients quasi-periodically depending on time
$t$, we show the reducibility (i.e., conjugation to time-independent) for a.e.
$E$. As an application of reducibility, we describe the behaviors of solution
in Sobolev space:
  -- Boundedness w.r.t. $t$ is always true for "most" $E\in{\mathcal I}$.
  -- For "generic" time-dependent perturbation, polynomial growth and
exponential growth to infinity w.r.t. $t$ occur for $E$ in a "small" part of
${\mathcal I}$.
  Concrete examples are given for which the growths of Sobolev norm do occur.

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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom