Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic growth of the local ground-state entropy of the ideal Fermi
  gas in a constant magnetic field   We consider the ideal Fermi gas of indistinguishable particles without spin
but with electric charge, confined to a Euclidean plane $\mathbb R^2$
perpendicular to an external constant magnetic field of strength $B>0$. We
assume this (infinite) quantum gas to be in thermal equilibrium at zero
temperature, that is, in its ground state with chemical potential $\mu\ge B$
(in suitable physical units). For this (pure) state we define its local entropy
$S(\Lambda)$ associated with a bounded (sub)region $\Lambda\subset \mathbb R^2$
as the von Neumann entropy of the (mixed) local substate obtained by reducing
the infinite-area ground state to this region $\Lambda$ of finite area
$|\Lambda|$. In this setting we prove that the leading asymptotic growth of
$S(L\Lambda)$, as the dimensionless scaling parameter $L>0$ tends to infinity,
has the form $L\sqrt{B}|\partial\Lambda|$ up to a precisely given (positive
multiplicative) coefficient which is independent of $\Lambda$ and dependent on
$B$ and $\mu$ only through the integer part of $(\mu/B-1)/2$. Here we have
assumed the boundary curve $\partial\Lambda$ of $\Lambda$ to be sufficiently
smooth which, in particular, ensures that its arc length $|\partial\Lambda|$ is
well-defined. This result is in agreement with a so-called area-law scaling
(for two spatial dimensions). It contrasts the zero-field case $B=0$, where an
additional logarithmic factor $\ln(L)$ is known to be present. We also have a
similar result, with a slightly more explicit coefficient, for the simpler
situation where the underlying single-particle Hamiltonian, known as the Landau
Hamiltonian, is restricted from its natural Hilbert space $\text L^2(\mathbb
R^2)$ to the eigenspace of a single but arbitrary Landau level. Both results
extend to the whole one-parameter family of quantum R\'enyi entropies.

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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
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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: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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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: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph