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When a continuous symmetry is spontaneously broken in non-relativistic theories, there appear Nambu-Goldstone (NG) modes, whose dispersion relations are either linear (type-I) or quadratic (type-II).
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A similar problem has been studied as the dependence of the relaxation dynamics with topological defects on the viscosity in P. Laguna and W. H. Zurek, “Critical dynamics of symmetry breaking: Quenches, dissipation, and cosmology” Phys. Rev. D 58
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2012
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L. Pollet and N. Prokof’ev, “Higgs Mode in a Two-Dimensiona Superfluid,” Phys. Rev. Lett. 109
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2013
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H. Watanabe and H. Murayama, “Effective Lagrangian for Nonrelativistic Systems,” Phys. Rev. X 4
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H. Watanabe and H. Murayama, “Noncommuting Momenta of Topological Solitons,” Phys. Rev. Lett. 112
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