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We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of $pi$ between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the intensity of the light that, because of the nonlinearity, affects the dynamics of the phase fluctuations. We interpret the results using methods of condensed matter physics, based on an effective description of the optical system. This interpretation sheds new light on the phenomena, facilitating the understanding of individual systems and leading to a framework for relating different problems with the same symmetry. In this context, we show that the perturbative excitations of the phase are Nambu-Goldstone bosons of a spontaneously broken $U(1)$ symmetry.
Phenomenological implications of a minimal extension to the Standard Model are considered, in which a Nambu-Goldstone boson emerges from the spontaneous breaking of a global U(1) symmetry. This is felt only by a scalar field which is a singlet under
We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semi-classical dynamics of the NG mo
We discuss symmetry breaking quantum phase transitions on the oft studied Bethe lattice in the context of the ferromagnetic scalar spherical model or, equivalently, the infinite $N_f$ limit of ferromagnetic models with $O(N_f)$ symmetry. We show that
Motivated by recent constructions of TeV-scale strongly-coupled dynamics, either associated with the Higgs sector itself as in pseudo-Nambu-Goldstone boson (pNGB) Higgs models or in theories of asymmetric dark matter, we show that stable solitonic Q-
We consider chiral perturbation theory in a finite volume and in a mixed regime of quark masses. We take N_l light quarks near the chiral limit, in the so-called epsilon-regime, while the remaining N_h quarks are heavier and in the standard p-regime.