Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality for free fermions and the local Weyl law for semiclassical
  Schr\"odinger operators   We study local asymptotics for the spectral projector associated to a
Schr\"odinger operator $-\hbar^2\Delta+V$ on $\mathbb{R}^n$ in the
semiclassical limit as $\hbar\to0$. We prove local uniform convergence of the
rescaled integral kernel of this projector towards a universal model, inside
the classically allowed region as well as on its boundary. This implies
universality of microscopic fluctuations for the corresponding free fermions
(determinantal) point processes, both in the bulk and around regular boundary
points. Our results apply for a general class of smooth potentials in arbitrary
dimension $n\ge 1$. We also obtain a central limit theorem which characterizes
the mesoscopic fluctuations of these Fermi gases in the bulk.

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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat