Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Validity of the Adiabatic Approximation   We analyze the validity of the adiabatic approximation, and in particular the
reliability of what has been called the "standard criterion" for validity of
this approximation. Recently, this criterion has been found to be insufficient.
We will argue that the criterion is sufficient only when it agrees with the
intuitive notion of slowness of evolution of the Hamiltonian. However, it can
be insufficient in cases where the Hamiltonian varies rapidly but only by a
small amount. We also emphasize the distinction between the adiabatic {\em
theorem} and the adiabatic {\em approximation}, two quite different although
closely related ideas.

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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex