E. Sadurni, J. A. Mendez-Bermudez
Periodic and disordered media are known to possess different transport properties, either classically or quantum-mechanically. This has been exhibited by effects such as Anderson localization in systems with disorder and the existence of photonic bandgaps in the periodic case. In this paper we analyze the transport properties of disordered waveguides with corners at very low frequencies, finding that the spectrum, conductance and wavefunctions are immune to disorder. Our waveguides are constructed by means of randomly oriented straight segments and connected by corners at right angles. Taking advantage of a trapping effect that manifests in the corner of a bent waveguide, we can show that a tight-binding approximation describes the system reasonably well for any degree of disorder. This provides a wide set of non-periodic geometries that preserve all the interesting transport properties of periodic media.
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http://arxiv.org/abs/1302.5835
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