Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and Vanishing of the Breathing Mode in Strongly Correlated
  Finite Systems   One of the fundamental eigenmodes of finite interacting systems is the mode
of {\em uniform radial expansion and contraction} -- the ``breathing'' mode
(BM). Here we show in a general way that this mode exists only under special
conditions: i) for harmonically trapped systems with interaction potentials of
the form $1/r^\gamma$ $(\gamma\in\mathbb{R}_{\neq0})$ or $\log(r)$, or ii) for
some systems with special symmetry such as single shell systems forming
platonic bodies. Deviations from the BM are demonstrated for two examples:
clusters interacting with a Lennard-Jones potential and parabolically trapped
systems with Yukawa repulsion. We also show that vanishing of the BM leads to
the occurence of multiple monopole oscillations which is of importance for
experiments.

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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas