Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum degeneracy of a circuit-QED system in the ultrastrong coupling
  regime   We investigate theoretically the quantum vacuum properties of a chain of $N$
superconducting Josephson atoms inductively coupled to a transmission line
resonator. We derive the quantum field Hamiltonian for such circuit-QED system,
showing that, due to the type and strength of the interaction, a quantum phase
transition can occur with a twice degenerate quantum vacuum above a critical
coupling. In the finite-size case, the degeneracy is lifted, with an energy
splitting decreasing exponentially with increasing values of $g^2 N^2$, where
$g$ is the dimensionless vacuum Rabi coupling per artificial atom. We determine
analytically the ultrastrong coupling asymptotic expression of the two
degenerate vacua for an arbitrary number of artificial atoms and of resonator
modes. In the ultrastrong coupling regime the degeneracy is protected with
respect to random fluctuations of the transition energies of the Josephson
elements.

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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc