29,160 research outputs found

    Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems

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    Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner

    Is the σ\sigma meson dynamically generated?

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    We study the problem whether the σ\sigma meson is generated `dynamically'. A pedagogical analysis on the toy O(N) linear sigma model is performed and we find that the large NcN_c limit and the mσ→∞m_\sigma\to \infty limit does not commute. The sigma meson may not necessarily be described as a dynamically generated resonance. On the contrary, the sigma meson may be more appropriately described by considering it as an explicit degree of freedom in the effective lagrangian.Comment: Contribution to ``Quark Confinement and Hadron Spectrum VII'', 2--7 Sept. 2006, Ponta Delgada, Acores, Portuga
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