Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binding of Polarons and Atoms at Threshold   If the polaron coupling constant $\alpha$ is large enough, bipolarons or
multi-polarons will form. When passing through the critical $\alpha_c$ from
above, does the radius of the system simply get arbitrarily large or does it
reach a maximum and then explodes? We prove that it is always the latter. We
also prove the analogous statement for the Pekar-Tomasevich (PT) approximation
to the energy, in which case there is a solution to the PT equation at
$\alpha_c$. Similarly, we show that the same phenomenon occurs for atoms, e.g.,
helium, at the critical value of the nuclear charge. Our proofs rely only on
energy estimates, not on a detailed analysis of the Schr\"odinger equation, and
are very general. They use the fact that the Coulomb repulsion decays like
$1/r$, while `uncertainty principle' localization energies decay more rapidly,
as $1/r^2$.

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The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an