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Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

Saad Yalouz and Vincent Pouthier*

  • Institut UTINAM, Univ. Bourgogne Franche-Comté, CNRS UMR 6213, 25030 Besançon Cedex, France

  • *vincent.pouthier@univ-fcomte.fr
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Phys. Rev. E 97, 022304 – Published 8 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022304

Abstract

A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.

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References (53)

  1. V. May and O. Kuhn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH Verlag, Berlin, 2000).
  2. T. Renger, V. May, and O. Kuhn, Phys. Rep. 343, 137 (2001).
  3. J. Knoester and V. M. Agranovich, Thin Films and Nanostructures: Electronic Excitations in Organic Based Nanostructures (Elsevier, Amsterdam, 2003).
  4. A. C. Scott, Phys. Rep. 217, 1 (1992).
  5. V. Pouthier, J. C. Light, and C. Girardet, J. Chem. Phys. 114, 4955 (2001).
  6. R. M. Pearlstein, J Chem. Phys. 56, 2431 (1972).
  7. D. L. Huber, Phys. Rev. B 20, 2307 (1979).
  8. D. L. Huber, Phys. Rev. B 22, 1714 (1980).
  9. P. E. Parris, Phys. Rev. Lett. 62, 1392 (1989).
  10. V. A. Malyshev, A. Rodriguez, and F. Dominguez-Adame, J. Lumin. 81, 127 (1999).
  11. D. L. Huber, Phys. Rev. B 45, 8947 (1992).
  12. R. S. Grinyov, A. V. Sorokin, G. Y. Gural'chuk, S. L. Efimova, I. A. Borovoi, and Y. V. Malyukin, Theor. Exp. Chem. 45, 58 (2009).
  13. V. M. Kenkre and Y. M. Wong, Phys. Rev. B 23, 3748 (1981).
  14. J. A. Tuszynski, M. F. Jorgensen, and D. Mobius, Phys. Rev. E 59, 4374 (1999).
  15. R. P. Hemenger, K. Lakatos-Lindenberg, and R. M. Pearlstein, J. Chem. Phys. 60, 3271 (1974).
  16. D. Astruc, E. Boisselier, and C. Ornelas, Chem. Rev. 110, 1857 (2010).
  17. R. E. Fenna and B. W. Matthews, Nature (London) 258, 573 (1975).
  18. K. Harigaya, Chem. Phys. Lett. 300, 33 (1999).
  19. M. A. Martin-Delgado, J. Rodriguez-Laguna, and G. Sierra, Phys. Rev. B 65, 155116 (2002).
  20. C. Supritz, A. Engelmann, and P. Reineker, J. Lumin. 111, 367 (2005).
  21. S. Tretiak, V. Chernyak, and S. Mukamel, J. Phys. Chem. B 102, 3310 (1998).
  22. M. Nakano, M. Takahata, H. Fujita, S. Kiribayashi, and K. Yamaguchi, Chem. Phys. Lett. 323, 249 (2000).
  23. G. W. Crabtree and N. S. Lewis, Phys. Today 60, 37 (2007).
  24. A. Bar-Haim, J. Klafter, and R. Kopelman, J. Am. Chem. Soc. 119, 6197 (1997).
  25. M. S. Choi, T. Aida, T. Yamazaki, and I. Yamazaki, Chem. Eur. J. 8, 2667 (2002).
  26. M. B. Plenio and S. F. Huelga, New. J. Phys. 10, 113019 (2008).
  27. M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, J. Chem. Phys. 129, 174106 (2008).
  28. P. Rebentrost, M. Mohseni, I. Kassal, S. Lloyd, and A. Aspuru-Guzik, New. J. Phys. 11, 033003 (2009).
  29. J. Wu, F. Liu, Y. Shen, J. Cao, and R. J. Silbey, New. J. Phys. 12, 105012 (2010).
  30. J. Wu, F. Liu, J. Ma, R. J. Silbey, and J. Cao, J. Chem. Phys. 137, 174111 (2012).
  31. O. Mulken and A. Blumen, Phys. Rep. 502, 37 (2011).
  32. A. M. Childs, Phys. Rev. Lett. 102, 180501 (2009).
  33. S. E. Venegas-Andraca, Quant. Inf. Process. 11, 1015 (2012).
  34. A. Volta, J. Phys. A: Math. Theor. 42, 225003 (2009).
  35. Z. Darazs, A. Anishchenko, T. Kiss, A. Blumen, and O. Mulken, Phys. Rev. E 90, 032113 (2014).
  36. X. P. Xu, Phys. Rev. E 79, 011117 (2009).
  37. P. L. Krapivsky, J. M. Luck, and K. Mallick, J. Stat. Phys. 154, 1430 (2014).
  38. E. Agliari, O. Mulken, and A. Blumen, Int. J. Bifurcation Chaos 20, 271 (2010).
  39. O. Mulken, A. Blumen, T. Amthor, C. Giese, M. Reetz-Lamour, and M. Weidemuller, Phys. Rev. Lett. 99, 090601 (2007).
  40. O. Mulken and A. Blumen, Physica E 42, 576 (2010).
  41. V. V. Sokolov and V. G. Zelevinsky, Nucl. Phys. A 504, 562 (1989).
  42. V. V. Sokolov and V. G. Zelevinsky, Ann. Phys. (NY) 216, 323 (1992).
  43. G. L. Celardo and L. Kaplan, Phys. Rev. B 79, 155108 (2009).
  44. R. H. Dicke, Phys. Rev. 93, 99 (1954).
  45. G. L. Celardo, F. Borgonovi, M. Erkli, V. I. Tsifrinovich, and G. P. Berman, J. Phys. Chem. C 116, 22105 (2012).
  46. G. G. Giusteri, G. L. Celardo, and F. Borgonovi, Phys. Rev. E 93, 032136 (2016).
  47. Y. Zhang, G. L. Celardo, F. Borgonovi, and L. Kaplan, Phys. Rev. E 95, 022122 (2017).
  48. A. Sequeira, Interconnecting Cisco Network Devices Part I (ICND1): Foundation Learning Guide (Cisco Press, Indianapolis, 2013).
  49. D. C. Brody, J. Phys. A: Math. Theor. 47, 035305 (2014).
  50. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, in Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing (STOC01) (ACM Press, New York, 2001), p. 50.
  51. O. Mulken and A. Blumen, Phys. Rev. E 73, 066117 (2006).
  52. O. Mulken, V. Bierbaum, and A. Blumen, J. Chem. Phys. 124, 124905 (2006).
  53. B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993).

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Phys. Rev. E 97, 022304– Published 8 February, 2018
  • Received 16 November 2017
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