Journal of the Korean Physical Society

, Volume 60, Issue 4, pp 665–668 | Cite as

Time reversibility of quantum diffusion in small-world networks

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Abstract

We study the time-reversal dynamics of a tight-binding electron in the Watts-Strogatz (WS) small-world networks. The localized initial wave packet at time t = 0 diffuses as time proceeds until the time-reversal operation, together with the momentum perturbation of the strength η, is made at the reversal time T. The time irreversibility is measured by I = |Π(t = 2T) − Π(t = 0)|, where Π is the participation ratio gauging the extendedness of the wavefunction and for convenience, t is measured forward even after the time reversal. When η = 0, the time evolution after T makes the wavefunction at t = 2T identical to the one at t = 0, and we find I = 0, implying a null irreversibility or a complete reversibility. On the other hand, as η is increased from zero, the reversibility becomes weaker, and we observe enhancement of the irreversibility. We find that I linearly increases with increasing η in the weakly-perturbed region, and that the irreversibility is much stronger in the WS network than in the local regular network.

Keywords

Small-world network Quantum diffusion Time-reversal dynamics 

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References

  1. [1]
    J. L. Lebowitz, Physica A. 263, 516 (1999).MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    C. Petitjean and Ph. Jacquod, Phys. Rev. Lett. 97, 124103 (2006).ADSCrossRefGoogle Scholar
  3. [3]
    H. S. Yamada and K. S. Ikeda, Phys. Rev. E 82, 060102(R) (2010).ADSCrossRefGoogle Scholar
  4. [4]
    M. Hiller, T. Kottos, D. Cohen and T. Geisel, Phys. Rev. Lett. 92, 010402 (2004).ADSCrossRefGoogle Scholar
  5. [5]
    G. Waldherr and G. Mahler, EPL 89, 40012 (2010).ADSCrossRefGoogle Scholar
  6. [6]
    D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).ADSCrossRefGoogle Scholar
  7. [7]
    O. Giraud, B. Georgeot and D. L. Shepelyansky, Phys Rev. E 72, 036203 (2005).ADSCrossRefGoogle Scholar
  8. [8]
    C-P. Zhu and S-J. Xiong, Phys. Rev. B 63, 193405 (2001).ADSCrossRefGoogle Scholar
  9. [9]
    R. Monasson, Eur. Phys. J. B 12, 555 (1999).ADSCrossRefGoogle Scholar
  10. [10]
    B. J. Kim, H. Hong and M. Y. Choi, Phys. Rev. B 68, 014304 (2003).ADSCrossRefGoogle Scholar
  11. [11]
    O. Mülken and A. Blumen, Phys Rev. E 73, 066117 (2006).ADSCrossRefGoogle Scholar
  12. [12]
    O. Mülken, V. Pernice and A. Blumen, Phys Rev. E 76, 051125 (2007).ADSCrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2012

Authors and Affiliations

  1. 1.Department of Physics and BK21 Physics Research DivisionSungkyunkwan UniversitySuwonKorea

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