Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical Completely Integrable Systems : Long-Time Dynamics And
  Observability Via Two-Microlocal Wigner Measures   We look at the long-time behaviour of solutions to a semi-classical
Schr\"odinger equation on the torus. We consider time scales which go to
infinity when the semi-classical parameter goes to zero and we associate with
each time-scale the set of semi-classical measures associated with all possible
choices of initial data. On each classical invariant torus, the structure of
semi-classical measures is described in terms of two-microlocal measures,
obeying explicit propagation laws. We apply this construction in two
directions. We first analyse the regularity of semi-classical measures, and we
emphasize the existence of a threshold : for time-scales below this threshold,
the set of semi-classical measures contains measures which are singular with
respect to Lebesgue measure in the "position" variable, while at (and beyond)
the threshold, all the semi-classical measures are absolutely continuous in the
"position" variable, reflecting the dispersive properties of the equation.
Second, the techniques of two- microlocal analysis introduced in the paper are
used to prove semiclassical observability estimates. The results apply as well
to general quantum completely integrable systems.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph