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Wave packet dynamics of two extended Harper models

Zhang Zhen-Jun Yu Miao Gong Long-Yan Tong Pei-Qing

Wave packet dynamics of two extended Harper models

Zhang Zhen-Jun, Yu Miao, Gong Long-Yan, Tong Pei-Qing
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  • We study the wave packet dynamics of two extended Harper models by using the second moment M2(t) and probability distribution Wn(t) numerically. The dynamical behaviors of two extended Harper models in all phases, on all phase boundary lines, and at the bicritical points are studied. For the first extended Harper model, we find that the wave packet is of ballistic diffusion in two metal phases, localized in the insulator phase, and of anomalous diffusion on the phase boundary lines and at the bicritical point. We also find the dynamical behavior on the boundary line of the metal-metal phase transition is the same as that on the metal-insulator phase transition. The spreading at the bicritical point is different from that on the phase boundary lines. For the second extended Harper model, we find that the wave packet is of ballistic diffusion in the metal phase, localized in the insulator phase, and of anomalous diffusion in the critical phase, on the phase boundary lines, and at the bicritical point. We also find the dynamical behavior on the boundary line of the critical-metal phase transition is similar to that at the bicritical point and the critical-insulator phase transition, but different from that of the metal-insulator phase transition.
    • Funds:
    [1]

    Shechtman D, Blech I, Gratias D, Cahn J W 1984 Phys. Rev. Lett. 53 1951

    [2]

    Levine D, Steinhardt P H 1984 Phys. Rev. Lett. 53 2477

    [3]

    Sokoloff J B 1985 Phys. Rep. 126 189

    [4]

    Albuquerque E L, Cottam M G 2003 Phys. Rep. 376 225

    [5]

    Aubry S, André G 1980 Ann. Isr. Phys. Soc. 3 133

    [6]

    Kohmoto M, Kadanoff L P, Tang C 1983 Phys. Rev. Lett. 50 1870

    [7]

    Song W G, Tong P Q 2009 Chin. Phys. B 18 4707

    [8]

    Luck J M 1989 Phys. Rev. B 39 5834

    [9]

    Luck J M 1993 J. Stat. Phys. 72 417

    [10]

    Tang C, Kohmoto M 1986 Phys. Rev. B 34 2041

    [11]

    Hiramoto H, Kohmoto M 1989 Phys. Rev. B 40 8225

    [12]

    Ng G S, Kottos T 2007 Phys. Rev. B 75 205120

    [13]

    Hofstadter D R 1976 Phys. Rev. B 14 2239

    [14]

    Nemec N, Cuniberti G 2006 Phys. Rev. B 74 165411

    [15]

    Nemec N, Cuniberti G 2007 Phys. Rev. B 75 201404

    [16]

    Wang J, Gong J B 2008 Phys. Rev. A 77 031405

    [17]

    Ino K, Kohmoto M 2006 Phys. Rev. B 73 205111

    [18]

    Chang I, Ikezawa K, Kohmoto M 1997 Phys. Rev. B 55 12971

    [19]

    Han J H, Thouless D J, Hiramoto H, Kohmoto M 1994 Phys. Rev. B 50 11365

    [20]

    Kohmoto M, Hasegawa Y 2007 Phys. Rev. B 76 205402

    [21]

    Izrailev F M, Kottos T, Politi A, Tsironis G P 1997 Phys. Rev. E 55 4951

    [22]

    Klymenko Yu, Shevtsov O 2008 Cond-mat/0806.4531v2

    [23]

    Nazareno H N, de Brito P E, Rodrigues E S 2007 Phy. Rev. B 76 125405

    [24]

    Zhu J M, Wang S J 2006 Acta Phys. Sin. 55 5018 (in Chinese) [祝敬敏、王顺金 2006 物理学报 55 5018]

    [25]

    Wang J M, Wang R, Zhang Y P, Liang J Q 2007 Chin. Phys. 16 2069

    [26]

    Flach S, Krimer D O, Skokos C H 2009 Phys. Rev. Lett. 102 024101

    [27]

    Hufnagel L, Ketzmerick R, Kottos T, Geisel T 2001 Phy. Rev. E 64 012301

    [28]

    Wang L F, Yang G C 2009 Chin. Phys. B 18 2523

    [29]

    Hatsugai Y, Kohmoto M 1990 Phy. Rev. B 42 8282

    [30]

    Zhou B H, Duan Z G, Zhou B L, Zhou G H 2010 Chin. Phys. B 19 037204

  • [1]

    Shechtman D, Blech I, Gratias D, Cahn J W 1984 Phys. Rev. Lett. 53 1951

    [2]

    Levine D, Steinhardt P H 1984 Phys. Rev. Lett. 53 2477

    [3]

    Sokoloff J B 1985 Phys. Rep. 126 189

    [4]

    Albuquerque E L, Cottam M G 2003 Phys. Rep. 376 225

    [5]

    Aubry S, André G 1980 Ann. Isr. Phys. Soc. 3 133

    [6]

    Kohmoto M, Kadanoff L P, Tang C 1983 Phys. Rev. Lett. 50 1870

    [7]

    Song W G, Tong P Q 2009 Chin. Phys. B 18 4707

    [8]

    Luck J M 1989 Phys. Rev. B 39 5834

    [9]

    Luck J M 1993 J. Stat. Phys. 72 417

    [10]

    Tang C, Kohmoto M 1986 Phys. Rev. B 34 2041

    [11]

    Hiramoto H, Kohmoto M 1989 Phys. Rev. B 40 8225

    [12]

    Ng G S, Kottos T 2007 Phys. Rev. B 75 205120

    [13]

    Hofstadter D R 1976 Phys. Rev. B 14 2239

    [14]

    Nemec N, Cuniberti G 2006 Phys. Rev. B 74 165411

    [15]

    Nemec N, Cuniberti G 2007 Phys. Rev. B 75 201404

    [16]

    Wang J, Gong J B 2008 Phys. Rev. A 77 031405

    [17]

    Ino K, Kohmoto M 2006 Phys. Rev. B 73 205111

    [18]

    Chang I, Ikezawa K, Kohmoto M 1997 Phys. Rev. B 55 12971

    [19]

    Han J H, Thouless D J, Hiramoto H, Kohmoto M 1994 Phys. Rev. B 50 11365

    [20]

    Kohmoto M, Hasegawa Y 2007 Phys. Rev. B 76 205402

    [21]

    Izrailev F M, Kottos T, Politi A, Tsironis G P 1997 Phys. Rev. E 55 4951

    [22]

    Klymenko Yu, Shevtsov O 2008 Cond-mat/0806.4531v2

    [23]

    Nazareno H N, de Brito P E, Rodrigues E S 2007 Phy. Rev. B 76 125405

    [24]

    Zhu J M, Wang S J 2006 Acta Phys. Sin. 55 5018 (in Chinese) [祝敬敏、王顺金 2006 物理学报 55 5018]

    [25]

    Wang J M, Wang R, Zhang Y P, Liang J Q 2007 Chin. Phys. 16 2069

    [26]

    Flach S, Krimer D O, Skokos C H 2009 Phys. Rev. Lett. 102 024101

    [27]

    Hufnagel L, Ketzmerick R, Kottos T, Geisel T 2001 Phy. Rev. E 64 012301

    [28]

    Wang L F, Yang G C 2009 Chin. Phys. B 18 2523

    [29]

    Hatsugai Y, Kohmoto M 1990 Phy. Rev. B 42 8282

    [30]

    Zhou B H, Duan Z G, Zhou B L, Zhou G H 2010 Chin. Phys. B 19 037204

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Publishing process
  • Received Date:  24 December 2009
  • Accepted Date:  17 December 2010
  • Published Online:  15 September 2011

Wave packet dynamics of two extended Harper models

  • 1. Department of Physics, Nanjing Normal University, Nanjing 210097, China

Abstract: We study the wave packet dynamics of two extended Harper models by using the second moment M2(t) and probability distribution Wn(t) numerically. The dynamical behaviors of two extended Harper models in all phases, on all phase boundary lines, and at the bicritical points are studied. For the first extended Harper model, we find that the wave packet is of ballistic diffusion in two metal phases, localized in the insulator phase, and of anomalous diffusion on the phase boundary lines and at the bicritical point. We also find the dynamical behavior on the boundary line of the metal-metal phase transition is the same as that on the metal-insulator phase transition. The spreading at the bicritical point is different from that on the phase boundary lines. For the second extended Harper model, we find that the wave packet is of ballistic diffusion in the metal phase, localized in the insulator phase, and of anomalous diffusion in the critical phase, on the phase boundary lines, and at the bicritical point. We also find the dynamical behavior on the boundary line of the critical-metal phase transition is similar to that at the bicritical point and the critical-insulator phase transition, but different from that of the metal-insulator phase transition.

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