Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical Study of the Soft Optic Mode Dynamics in a Relaxor
  Ferroelectric. The Effect of Polar Nanoregions   We propose a simple and solvable mean-field model of the scattering of
transverse optic modes by Polarized Nano Regions (PNR) in the paraelectric
phase of relaxor ferroelectrics. The PNR is assumed to be a ferroelectric
sphere embedded in the host isotropic medium. The Lagrangian parameters are
taken to be the same inside and outside the PNR, with exception of the
soft-mode gap temperature dependence. The interaction of the Transverse (TO)
with the longitudinal (LO) optic modes is taken into account but the latter is
found to be important only at the surface of the PNR. Elementary excitations of
the system are found to be of two types - Vortex (V) and Quasi Polar (QP). V
excitations correspond to closed polarization lines or closed TO displacements
while QP excitations contain open TO polarization lines, with an electric
dipole if the net angular momentum j=1. LO waves are virtually excited only in
the thin layer near the PNR surface and can be excluded from the boundary
conditions without any consequence. The final boundary conditions include only
V and QP TO wave amplitudes. Dynamical equations are solved and a phase diagram
is predicted. The phase transition temperature is found to be lower for Vortex
than for QP excitations. Therefore, the QP condensation (local phase
transition) occurs before the Vortex one upon cooling. TO scattering by the PNR
reveals strong long-wave resonances that can be shown to result from shallow
localized and quasi-localized states and may be essential to understanding the
waterfall observed in TO studies by inelastic neutron scattering.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga