Scattering from isospectral graphs.
Seminar Room 1, Newton Institute
AbstractIn 1966 Marc Kac asked 'Can one hear the shape of a drum?'. The answer was given only in 1992, when Gordon et al. found a pair of drums with the same spectrum. The study of isospectrality and inverse problems is obviously not limited to drums and treats various objects such as molecules, quantum dots and graphs. In 2005 Okada et al. conjectured that isospectral drums can be distinguished by their scattering poles (resonances). We prove that this is not the case for isospectral quantum graphs, i.e., isospectral quantum graphs share the same resonance distribution. This is a joint work with Adam Sawicki and Uzy Smilansky.
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