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Are Scattering Properties of Networks Uniquely Connected to Their Shapes?

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Abstract

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.

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Author information

Authors and Affiliations

  1. Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland

    Oleh Hul, Michał Ławniczak, Szymon Bauch & Leszek Sirko

  2. Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland

    Adam Sawicki & Marek Kuś

Authors
  1. Oleh Hul
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  2. Michał Ławniczak
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  3. Szymon Bauch
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  4. Adam Sawicki
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  5. Marek Kuś
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  6. Leszek Sirko
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Corresponding author

Correspondence to Leszek Sirko .

Editor information

Editors and Affiliations

  1. , Institut für Theoretische Physik IV, Heinrich-Heine-Universität, Universitätsstrasse 1, Düsseldorf, 40225, Germany

    Reinhold Egger

  2. Laboratory for Advanced Studies, Department of Energy, Turin Polytechnic University in Tashkent, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Davron Matrasulov

  3. , Department of Physics, National University of Uzbekistan, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Khamdam Rakhimov

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Hul, O., Ławniczak, M., Bauch, S., Sawicki, A., Kuś, M., Sirko, L. (2013). Are Scattering Properties of Networks Uniquely Connected to Their Shapes?. In: Egger, R., Matrasulov, D., Rakhimov, K. (eds) Low-Dimensional Functional Materials. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6618-1_10

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