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Resonances in Quantum Networks and Their Generalizations

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Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale

Abstract

We discuss resonances in quantum graphs and their more general analogs having ‘edges’ of different dimensions. Since the notion of resonance may mean different things, we show that the two most common definitions, scattering and resolvent resonances, are equivalent in this case. We analyze the high-energy behavior of resonances in quantum graphs and show that it may deviate from the standard Weyl law prediction; we derive a criterion which shows when such a thing happens. We also investigate influence of magnetic fields on graph resonances and show that they are field configurations which remove all ‘true’ resonances from such systems.

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Acknowledgements

The research the results of which are reported here has been supported by the Czech Science Foundation within the project P203/11/0701.

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Authors and Affiliations

  1. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519, Prague, Czech Republic

    Pavel Exner

  2. Nuclear Physics Institute, ASCR, 25068, Řež near Prague, Czech Republic

    Pavel Exner

Authors
  1. Pavel Exner
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Correspondence to Pavel Exner .

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Editors and Affiliations

  1. Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan

    Davron Matrasulov

  2. Department of Physics, Boston University, Boston, Massachusetts, USA

    H. Eugene Stanley

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Exner, P. (2014). Resonances in Quantum Networks and Their Generalizations. In: Matrasulov, D., Stanley, H. (eds) Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale. NATO Science for Peace and Security Series C: Environmental Security. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8704-8_12

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  • DOI: https://doi.org/10.1007/978-94-017-8704-8_12

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8703-1

  • Online ISBN: 978-94-017-8704-8

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