Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ballistic transport for limit-periodic Schr\"odinger operators in one
  dimension   In this paper, we consider the transport properties of the class of
limit-periodic continuum Schr\"odinger operators whose potentials are
approximated exponentially quickly by a sequence of periodic functions. For
such an operator $H$ and $X_H(t)$ the Heisenberg evolution of the position
operator, we show the limit of $\frac{1}{t}X_H(t)\psi$ as $t\to\infty$ exists
and is nonzero for $\psi\ne 0$ belonging to a dense subspace of initial states
which are sufficiently regular and of suitably rapid decrease. This is viewed
as a particularly strong form of ballistic transport, and this is the first
time it has been proven in a continuum almost periodic non-periodic setting. In
particular, this statement implies that for the initial states considered, the
second moment grows quadratically in time.

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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
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The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th