Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two diverging length scales in the structure of jammed packings   At densities higher than the jamming transition for athermal, frictionless
repulsive spheres we find two distinct length scales, both of which diverge as
a power law as the transition is approached. The first, $\xi_{Z}$, is
associated with the two-point correlation function for the number of contacts
on two particles as a function of the particle separation. The second,
$\xi_{f}$, is associated with contact-number fluctuations in subsystems of
different sizes. On scales below $\xi_{f}$ the fluctuations are highly
suppressed, similar to the phenomenon of hyperuniformity usually associated
with density fluctuations. The exponents for the divergence of $\xi_{Z}$ and
$\xi_{f}$ are different and appear to be different in two and three dimensions.

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The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat