Advertisement

Accurate measurement of the localization properties of electric transmission lines using the overlap amplitude

  • Edmundo LazoEmail author
Regular Article

Abstract

We determine the localization properties of classic direct electric transmission lines by means of the overlap amplitude. The amplitude is defined as C i,j ω = 2|I i ω I j ω |, where I i ω is the electric current in the ith cell of the transmission line for the state with frequency ω. This definition is motivated by the concurrence C i,j α = 2|φ i α φ j α |, which is a quantum correlation measure (pairwise entanglement). We distribute the inductances L j according to three non-linear models: (a) the slowly varying potential model; (b) the Aubry-André model and (c) the Soukoulis-Economou model. The results show that the average of the powers of the overlap amplitude ⟨(C i,j ω )2q ⟩ and its scaling properties may accurately characterize the localization behavior of these non-linear models. Moreover, the overlap amplitude can be used to determine the mobility edge of some non-periodic models.

Graphical abstract

Keywords

Quantum Information 

References

  1. 1.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    D.H. Dunlap, H.L. Wu, P.W. Philips, Phys. Rev. Lett. 65, 88 (1990)ADSCrossRefGoogle Scholar
  3. 3.
    P.W. Philips, H.-L. Wu, Science 252, 1805 (1991)ADSCrossRefGoogle Scholar
  4. 4.
    E. Lazo, M.E. Onell, Physica B 299, 173 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    F.A.B.F. de Moura, M.L. Lyra, Phys. Rev. Lett. 81, 3735 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    S.S. Albuquerque, F.A.B.F. de Moura, M.L. Lyra, Physica A 357, 165 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    F.A.B.F. de Moura, L.P. Viana, A.C. Frery, Phys. Rev. B 73, 212302 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    F.A.B.F. de Moura, Int. J. Mod. Phys. C 22, 63 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    S.S. Albuquerque, J.L.L. dos Santos, F.A.B.F. de Moura, M.L. Lyra, J. Phys.: Condens. Matter 27, 175401 (2015)ADSGoogle Scholar
  11. 11.
    J.L.L. dos Santos, B.P. Nguyen, F.A.B.F. de Moura, Physica A 435, 15 (2015)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    E. Diez, F. Izrailev, A.A. Krokhin, A. Rodriguez, Phys. Rev. B 78, 035118 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    E. Lazo, E. Diez, Phys. Lett. A 374, 3538 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    E. Lazo, E. Diez, Phys. Lett. A 375, 2122(2011)ADSCrossRefGoogle Scholar
  15. 15.
    E. Lazo, F. Mellado, E. Saavedra, Phys. Lett. A 376, 3423 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    E. Lazo, E. Diez, Physica B 419, 19 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    E. Lazo, F.R. Humire, E. Saavedra, Physica B 452, 74 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    E. Lazo, E. Saavedra, F.R. Humire, C.E. Castro, F. Cortés, Eur. Phys. J. B 88, 216 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    E. Lazo, C. Castro, F. Cortés-Cortés, Phys. Lett. A 380, 3284 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    E. Lazo, A. Garrido, F. Neira, Eur. Phys. J. B 89, 249 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    S. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 133 (1980)Google Scholar
  22. 22.
    C.M. Soukoulis, E.N. Economou, Phys. Rev. Lett. 48, 1043 (1982)ADSCrossRefGoogle Scholar
  23. 23.
    S. Das Sarma, S. He, X.C. Xie, Phys. Rev. Lett. 61, 2144 (1988)ADSCrossRefGoogle Scholar
  24. 24.
    H. Hiramoto, M. Kohmoto, Phys. Rev. B 40, 8225 (1989)ADSCrossRefGoogle Scholar
  25. 25.
    S. Das Sarma, S. He, X.C. Xie, Phys. Rev. B 41, 5544 (1990)ADSCrossRefGoogle Scholar
  26. 26.
    P.Q. Zhou, X.J. Fu, Z.Z. Guo, Y.Y. Liu, Z. Phys. B: Condens. Matter 100, 321 (1996)ADSCrossRefGoogle Scholar
  27. 27.
    L. Gong, H. Zhu, S. Zhao, W. Cheng, Phys. Lett. A 376, 3026 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    F.M. Izrailev, A.A. Krokhin, N.M. Makarov, Phys. Rep. 512, 125 (2012)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    W.W. Cheng, L.Y. Gong, C.J. Shan, Y.B. Sheng, S.M. Zhao, Eur. Phys. J. D 67, 121, (2013)ADSCrossRefGoogle Scholar
  30. 30.
    W.W. Cheng, C.J. Shan, L.Y. Gong, S.M. Zhao, J. Phys. B 47, 175503 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    L. Gong, W. Li, S. Zhao, W. Cheng, Phys. Lett. A 380, 59 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    U. Kuhl, F.M. Izrailev, A.A. Krokhin, H.-J. Stöckmann, Appl. Phys. Lett. 77, 633 (2000)ADSCrossRefGoogle Scholar
  33. 33.
    A.A. Krokhin, F.M. Izrailev, U. Kuhl, H.-J. Stöckmann, S.E. Ulloa, Physica E 13, 695 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    U. Kuhl, F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 100, 126402 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, Y. Silbergerg, Phys. Rev. Lett. 103, 013901 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    Y.E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, O. Zilbergerg, Phys. Rev. Lett. 109, 106402 (2012)ADSCrossRefGoogle Scholar
  37. 37.
    M. Verbin, O. Zilbergerg, Y.E. Kraus, Y. Lahini, Y. Silbergerg, Phys. Rev. Lett. 110, 076403 (2013)ADSCrossRefGoogle Scholar
  38. 38.
    L. Dal Negro, C.J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Laguendijk, R. Righini, M. Colocci, D.S. Wiersma, Phys. Rev. Lett. 90, 055501 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    G. Roati, C. Derrico, L. Fallani, M. Fattori, C. Fort, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    G. Modugno, Rep. Prog. Phys. 73, 102401 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, P. Bouyer, Nat. Phys. 8, 398 (2012)CrossRefGoogle Scholar
  42. 42.
    K. Tanaka, S.-I. Nakayama, J. Optoelectron. Adv. Mater. 2, 5 (2000)Google Scholar
  43. 43.
    S.S. Apostolov, F.M. Izrailev, N.M. Makarov, Z.A. Mayzelis, S.S. Melnyk, O.V. Usatenko, J. Phys. A: Math. Theor. 41, 175101 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    S. Hill, W.K. Wootters, Phys. Rev. Lett. 78, 5022 (1997)ADSCrossRefGoogle Scholar
  45. 45.
    W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    V. Coffman, J. Kundu, W.K. Wootters, Phys. Rev. A 61, 052306 (2000)ADSCrossRefGoogle Scholar
  47. 47.
    A. Lakshminarayan, V. Subrahmanyam, Phys. Rev. A 67, 052304 (2003)ADSCrossRefGoogle Scholar
  48. 48.
    H. Li, X. Wang, B. Hu, J. Phys. A: Math. Gen. 37, 10665 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    X. Wang, H. Li, B. Hu, Phys. Rev. A 69, 054303 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    Y. Shi, J. Phys. A 37, 6807 (2004)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    L. Gong, P. Tong, Chin. Phys. Lett. 22, 2759 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    L. Gong, P. Tong, Phys. Rev. A 71, 042333 (2005)ADSCrossRefGoogle Scholar
  53. 53.
    H. Li, X. Wang, Mod. Phys. Lett. B 19, 517 (2005)ADSCrossRefGoogle Scholar
  54. 54.
    L. Gong, Y. Zheng, H. Wang, W. Cheng, S. Zhao, Eur. Phys. J. B 87, 193 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    H. Cruz, S. Das Sarma, J. Phys. France 31, 1515 (1993)CrossRefGoogle Scholar
  56. 56.
    L. Zhang, L.Y. Gong, P.Q. Tong, Eur. Phys. J. B 80, 485 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    L.Y. Gong, P.Q. Tong, Phys. Rev. A 71, 042333 (2005)ADSCrossRefGoogle Scholar
  58. 58.
    L.Y. Gong, L. Wei, S.M. Zhao, W.W. Cheng, Phys. Rev. E 86, 061122 (2012)ADSCrossRefGoogle Scholar
  59. 59.
    L. Gong, H. Zhu, W. Cheng, Y. Sheng, Phys. Lett. A 376, 3026 (2012)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Departamento de Física, Facultad de Ciencias, Universidad de TarapacáD AricaChile

Personalised recommendations