Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transition in Space: How Far Does a Symmetry Bend Before It
  Breaks?   We extend the theory of symmetry breaking dynamics in non-equilibrium second
order phase transitions known as the Kibble-Zurek mechanism (KZM) to
transitions where the change of phase occurs not in time, but in space. This
can be due to a time-independent spatial variation of a field that imposes a
phase with one symmetry to the left of where it attains critical value, while
allowing spontaneous symmetry breaking to the right of that critical
borderline. Topological defects need not form in such a situation. We show,
however, that the size, in space, of the ``scar'' over which the order
parameter adjusts as it ``bends'' interpolating between the phases with
different symmetry follows from a KZM - like approach. As we illustrate on the
example of a transverse quantum Ising model, in quantum phase transitions this
spatial scale -- the size of the scar -- is directly reflected in the energy
spectrum of the system: In particular, it determines the size of the energy
gap.

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The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg