Journal of the Korean Physical Society

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

Time reversibility of quantum diffusion in small-world networks

  • Sung-Guk Han
  • Beom Jun Kim


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.


Small-world network Quantum diffusion Time-reversal dynamics 


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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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