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Schrödinger and Dirac dynamics on time-dependent quantum graph

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Abstract

Quantum graphs with varying edges lengths are constructed. We deal with two types of operators on the graph edges: the Schrödinger and the Dirac operators. The dynamics of quantum particles for these two cases is compared. From the physical point of view, the Schrödinger dynamics corresponds to nonrelativistic particle and the Dirac dynamics to the relativistic one.

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References

  1. S Gnutzmann and U Smilansky Adv.Phys. 55 527 (2006)

    Article  ADS  Google Scholar 

  2. P Kuchment and L Kunyansky Adv. Comput. Math. 16 263 (2002)

    Article  MathSciNet  Google Scholar 

  3. P Exner, P Keating, P Kuchment, T Sumada and A Teplyaev Analysis on graph and its applications (Providence: AMS) Sec. 4 (2008)

  4. P Exner, J. Phys. A: Math. Gen., 21 4009 (1988).

    Article  ADS  Google Scholar 

  5. P Exner and P Seba Rep. Math. Phys. 28 7 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  6. N I Gerasimenko and B S Pavlov Theoret. Math. Phys. 74 230 (1988)

    Article  MathSciNet  Google Scholar 

  7. I Y Popov, J. Math. Phys. 55 033504 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  8. I Y Popov and P I Smirnov Phys. Lett. A 377 439 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  9. P.Kuchment, G. Berkolaiko, Introduction to Quantum Graphs, (Providence: AMS) (2013).

  10. J V Jose and R Gordery Phys. Rev. Lett. 56 290 (1986)

    Article  ADS  Google Scholar 

  11. A J Makowski and S T Dembinski Phys. Lett. 154 217 (1991)

    Article  MathSciNet  Google Scholar 

  12. A Munier, J R Burgan, M Feix and E Fijalkow J. Math. Phys. 22 1219 (1981)

  13. P Pereshogin and P Pronin Phys. Lett., 156 12 (1991)

    Article  Google Scholar 

  14. M Correggi, G Dell’Antonio, R Figari, A Mantile Commun. Math. Phys. 257 169 (2005)

  15. T Hmidi, A Mantile and F. Nier Math. Phys. Anal. Geom. 13 83 (2009)

  16. C Cacciapuoti, A Mantile and A Posilicano Nanosystems: Phys. Chem. Math. 7 303 (2016)

  17. G F Dell’Antonio, R Figari and A Teta J. Funct. Anal. 142 249 (1996)

  18. B M Levitan, I S Sargsyan Sturm-Liouville and Dirac Operators (Berlin: Springer) (1991)

  19. V Alonso, S De Vincenzo and L Mondino Eur. J. Phys. 18 315 (1997)

  20. V Alonso, S De Vincenzo and L Mondino J. Phys. A 30 8573 (1997).

  21. V Alonso and S De Vincenzo J. Phys. A 32 5277 (1999).

  22. Z A Sobirov, D U Matrasulov, Sh Ataev and H Yusupov In Complex Phenomena in Nanoscale Systems. Eds. G. Casati, D. Matrasulov (Berlin: Springer) (2009)

  23. F Bayazit, B Dorn and M Kramar Fijavz Networks and Heterogeneous Media 8 843 (2013)

  24. W Arendt, D Dier and M Kramar Fijavz Appl. Math. Optim. 69 315 (2014)

  25. D N Pinder Am. J. Phys. 58 54 (1990).

    Article  ADS  Google Scholar 

  26. D U Matrasulov, J R Yusupov, K K Sabirov and Z A Sobirov Nanosystems: Phys. Chem. Math. 6 173 (2015)

  27. D A Eremin, E N Grishanov, O G Kostrov, D S Nikiforov and I Y Popov Nanosyst.: Phys. Chem. Math. 8 420 (2017)

  28. F Gesztesy, H Grosse and B Thaller hys. Rev. Lett. 50, 625 (1983)

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Acknowledgements

This work was partially financially supported by the Government of the Russian Federation (Grant 08-08), by Grant 16-11-10330 of Russian Science Foundation.

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Authors and Affiliations

  1. ITMO University, Kronverkskiy, 49, St. Petersburg, Russia, 197101

    D S Nikiforov, I V Blinova & I Y Popov

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  1. D S Nikiforov
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  2. I V Blinova
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  3. I Y Popov
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Correspondence to I Y Popov.

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Nikiforov, D.S., Blinova, I.V. & Popov, I.Y. Schrödinger and Dirac dynamics on time-dependent quantum graph. Indian J Phys 93, 913–920 (2019). https://doi.org/10.1007/s12648-018-1352-8

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  • DOI: https://doi.org/10.1007/s12648-018-1352-8

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