Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schr\"odinger equations with time-dependent strong magnetic fields   We consider d-dimensional time dependent Schr\"odinger equations on the
Hilbert space of square integrable functions. We assume magnetic and scalar
potentials are almost critically singular with respect to spatial variables
both locally and at infinity for the fixed time Schr\"odinger operator H(t) to
be essentially self-adjoint on the compactly supported smooth functions. In
particular, if magnetic field B(t,x) is very strong at infinity, the scalar
potential can explode to negative infinity faster than quadratic functions. We
show that equations uniquely generate unitary propagators under suitable
conditions on the size and singularities of time derivatives of potentials.
Basic tools are Kato's abstract theory for evolution equations, Iwatsuka's
identity which rewrites H(t) to an elliptic differential operator in which
B(t,x) appears explicitly, and a new diamagnetic like inequality.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nlin
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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: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas