Scattering of vibrational waves in perturbed quasi-one-dimensional multichannel waveguides

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Abstract
We investigate the scattering properties of vibrational waves in perturbed quasi-one-dimensional multichannel waveguides in the harmonic approximation. Local defects are introduced by changing the masses or the spring constants of the perfect waveguide. For both types of defects we find resonances in the continuum. These are due to the coherent coupling between local defect states and propagating states. Beyond the similarity with the quantum-mechanical case of electron scattering and associated Fano resonances, the scattering behavior of vibrational waves appears to be more complex. This complexity can be attributed to the vector character of the vibrational amplitudes and to additional possibilities for mode-mode coupling by the defects. To illustrate the method a detailed discussion of the transmission spectra is presented for the generic case of a double chain containing defects, which shows already the essential characteristic features of a multichannel system.