Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions for a collective coordinate coupled to Luttinger
  liquids   We study various realizations of collective coordinates, e.g. the position of
a particle, the charge of a Coulomb box or the phase of a Bose or a
superconducting condensate, coupled to Luttinger liquids (LL) with N flavors.
We find that for Luttinger parameter 1/2<K<1 there is a phase transition from a
delocalized phase into a phase with a periodic potential at strong coupling. In
the delocalized phase the dynamics is dominated by an effective mass, i.e.
diffusive in imaginary time, while on the transition line it becomes
dissipative. At K=1/2 there is an additional transition into a localized phase
with no diffusion at zero temperature.

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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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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: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex