Are Scattering Properties of Networks Uniquely Connected to Their Shapes?

Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)


Are scattering properties of networks uniquely connected to their shapes? This is a modification of the famous question of Mark Kac “Can one hear the shape of a drum: revisited. which can be asked in the case of scattering systems such as quantum graphs and microwave networks. We present the experimental approach to this problem (Hul et al., Phys Rev Lett 109:040402, 2012). Our experimental results indicate a negative answer to the above question. To demonstrate this we constructed a pair of isospectral microwave networks consisting of vertices connected by microwave coaxial cables and extended them to scattering systems by connecting leads to infinity to form isoscattering networks. We show that the amplitudes and phases of the determinants of the scattering matrices of such networks are the same within the experimental uncertainties. Additionally, we demonstrate that the scattering matrices of the networks are conjugated by the transplantation relation. The experimental results are in perfect agreement with the theoretical predictions.


Helmholtz Equation Coaxial Cable Vector Network Analyzer Quantum Graph Microwave Cavity 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of PhysicsPolish Academy of SciencesWarszawaPoland
  2. 2.Center for Theoretical PhysicsPolish Academy of SciencesWarszawaPoland

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