Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Purity and Quantum Phase Transition for Bose-Einstein
  condensates in a Symmetric Double Well   The generalized purity is employed for investigating the process of coherence
loss and delocalization of the Q-function in the Bloch sphere of a two-mode
Bose-Einstein condensate in a symmetrical double well with cross-collision.
Quantum phase transition of the model is signaled by the generalized purity as
a function of an appropriate parameter of the Hamiltonian and the number of
particles (N). A power law dependence of the critical parameter with N is
derived.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph