Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean Field Limits in Strongly Confined Systems   We consider the dynamics of $N$ interacting bosons in three dimensions which
are strongly confined in one or two directions. We analyze the two cases where
the interaction potential $w$ is rescaled by either $N^{-1}w(\cdot)$ or
$a^{3\theta-1}w(a^\theta \cdot)$ and choose the initial wavefunction to be
close to a product wavefunction. For both scalings we prove that in the mean
field limit $N\rightarrow \infty $ the dynamics of the $N$-particle system are
described by a nonlinear equation in one or two dimensions. In the case of the
scaling $N^{-1}w(\cdot)$ this equation is the Hartree equation and for the
scaling $a^{3\theta-1}w(a^\theta \cdot) $ the nonlinear Schr\"odinger equation.
In both cases we obtain explicit bounds for the rate of convergence of the
$N$-particle dynamics to the one-particle dynamics.

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The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics