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Physics on Graphs

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Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale

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Abstract

This is an extended version of the talk given at the Nato Advanced Research Workshop: New Challenges in Complex System Physics, May 20–24, 2013 in Samarkand (Uzbekistan). We report on results on three topics in joint work with V. Kostrykin (Mainz, Germany) and J. Potthoff (Mannheim, Germany):

  • Propagation of waves on graphs,

  • Brownian motion on graphs,

  • One particle quantum dynamics on graphs.

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References

  1. Kostrykin V, Schrader R (1999) Kirchhoff’s rule for quantum wires. J Phys A: Math Gen 32:595–630

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Kostrykin V, Potthoff J, Schrader R (2012) Finite propagation speed for solutions of the wave equation on metric graphs. J Funct Anal 263:1198–1223

    Article  MATH  MathSciNet  Google Scholar 

  3. Schrader R (2009) Finite propagation speed and causal free quantum fields on networks. J Phys A: Math Gen 42:495401

    Article  MathSciNet  Google Scholar 

  4. Kostrykin V, Potthoff J, Schrader R (2012) Brownian motion on metric graphs. J Math Phys 53:095206. Special Issue in Honor of Elliott Lieb’s 80th Birthday

    Google Scholar 

  5. Kostrykin V, Potthoff J, Schrader R (2012) Construction of the paths of Brownian motion on star graphs I. Commun Stoch Anal 6:223–245

    MathSciNet  Google Scholar 

  6. Kostrykin V, Potthoff J, Schrader R (2012) Construction of the paths of Brownian motion on star graphs II. Commun Stoch Anal 6:247–261

    MathSciNet  Google Scholar 

  7. Kostrykin V, Schrader R (2000) Kirchhoff’s rule for quantum wires, II: the inverse problem with possible applications to quantum computers. Fortschr d Phys 48:703–716

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Kostrykin V, Schrader R (2001) The generalized star product and the factorization of scattering matrices on graphs. J Math Phys 42:1563–1598

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Kostrykin V, Schrader R (2003) Quantum wires with magnetic fluxes. Commun Math Phys 237:161–179

    ADS  MATH  MathSciNet  Google Scholar 

  10. Kostrykin V, Schrader R (2006) Laplacians on metric graphs: eigenvalues, resolvents and semigroups. In: Berkolaiko G, Carlson R, Fulling SA, Kuchment P (eds) Quantum graphs and their applications (proceedings of joint summer research conference in the mathematical sciences on quantum graphs and their applications, Snowbird, 2005). Contemporary mathematics, vol 415. American Mathematical Society, Providence, pp 201–225

    Google Scholar 

  11. Kostrykin V, Potthoff J, Schrader R (2007) Heat kernels on metric graphs and a trace formula. In: Germinet F, Hislop PD (eds) Adventures in mathematical physics. Contemporary mathematics, vol 447. American Mathematical Society, Providence, pp 175–198

    Chapter  Google Scholar 

  12. Kostrykin V, Potthoff J, Schrader R (2008) Contraction semigroups on metric graphs. In: Exner P, Keating J, Sunada T, Teplyaev A (eds) Analysis on graphs and its applications. Proceedings of symposia in pure mathematics, vol 77. American Mathematical Society, Providence, pp 423–458

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195, Berlin, Germany

    Robert Schrader

Authors
  1. Robert Schrader
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Correspondence to Robert Schrader .

Editor information

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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Schrader, R. (2014). Physics on Graphs. 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_11

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  • DOI: https://doi.org/10.1007/978-94-017-8704-8_11

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8703-1

  • Online ISBN: 978-94-017-8704-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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