Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Disordered Solids Without Well-Defined Transverse Phonons: The Nature of
  Hard Sphere Glasses   We probe the Ioffe-Regel limits of glasses with repulsions near the
zero-temperature jamming transition by measuring the dynamical structure
factors. At zero temperature, the transverse Ioffe-Regel frequency vanishes at
the jamming transition with a diverging length, but the longitudinal one does
not, which excludes the existence of a diverging length associated with the
longitudinal excitations. At low temperatures, the transverse and longitudinal
Ioffe-Regel frequencies approach zero at the jamming-like transition and glass
transition, respectively. As a consequence, glasses between the glass
transition and jamming-like transition, which are hard sphere glasses in the
low temperature limit, can only carry well-defined longitudinal phonons and
have an opposite pressure dependence of the ratio of the shear modulus to the
bulk modulus from glasses beyond the jamming-like transition.

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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph