Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observability and Controllability for the Schr{\"o}dinger Equation on
  Quotients of Groups of Heisenberg Type   We give necessary and sufficient conditions for the controllability of a
Schr\''odinger equation involving the sub-Laplacian of a nilmanifold obtained
by taking the quotient of a group of Heisenberg type by one of its discrete
sub-groups.This class of nilpotent Lie groups is a major example of stratified
Lie groups of step 2. The sub-Laplacian involved in these Schr\''odinger
equations is subelliptic, and, contrarily to what happens for the usual
elliptic Schr\''odinger equation for example on flat tori or on negatively
curved manifolds, there exists a minimal time of controllability. The main
tools used in the proofs are (operator-valued) semi-classical measures
constructed by use of representation theory and a notion of semi-classical wave
packets that we introduce here in the context of groups of Heisenberg type.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: nlin