Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smoothing of transport plans with fixed marginals and rigorous
  semiclassical limit of the Hohenberg-Kohn functional   We prove rigorously that the exact N-electron Hohenberg-Kohn density
functional converges in the strongly interacting limit to the strictly
correlated electrons (SCE) functional, and that the absolute value squared of
the associated constrained-search wavefunction tends weakly in the sense of
probability measures to a minimizer of the multi-marginal optimal transport
problem with Coulomb cost associated to the SCE functional. This extends our
previous work for N=2 [CFK11]. The correct limit problem has been derived in
the physics literature by Seidl [Se99] and Seidl, Gori-Giorgi and Savin
[SGS07]; in these papers the lack of a rigorous proof was pointed out.
  We also give a mathematical counterexample to this type of result, by
replacing the constraint of given one-body density -- an infinite-dimensional
quadratic expression in the wavefunction -- by an infinite-dimensional
quadratic expression in the wavefunction and its gradient. Connections with the
Lawrentiev phenomenon in the calculus of variations are indicated.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th