Cantor型人工DNA序列的关联属性及输运性质

刘小良; 梁亮文; 徐慧; 李江

doi:10.7498/aps.60.077201

摘要

对按膨胀规律A→ABA和B→BBB生成的有限长度Cantor型人工DNA序列,采用统计方法研究了序列的净位移及其标准偏差、重标极差函数及其Hurst指数,并将结果与一维随机二元序列进行了对比,直接论证了Cantor序列具有关联、标度不变及自相似等性质.从Anderson紧束缚模型出发,采用重整化群方法研究了该序列的电子输运特性.研究表明具有好的输运效率的扩展态能在较宽的能量区间上存在,随着序列长度的增加,扩展态的能量区间变得更为细碎,但具有好的透射性的电子态数量只是略有减少,共振能态可以在较长的序列中存在

关键词:

Abstract

For the Cantor-styled artificial DNA sequence constructed by following the inflation rule A→ABA and B→BBB, using the one-dimensional random walk model and Hurst analysis, we calculate numerically the displacement and its standard deviation, the rescaled range function and the Hurst exponent. The results are compared with those of one-dimensional random binary sequence. We show that Cantor-styled DNA sequence presents correlated behavior, scaling invariability, and self-similarity. In addition, according to the renormalization-group method, we study the charge transfer properties of Cantor-styled DNA sequence, including localization length, charge transmission coefficient and Lyapunov exponent. We find that some resonant peaks can survive in relatively long Cantor-styled DNA sequences, which also implies that there are long-range correlations in Cantor-styled DNA sequences.

Keywords:

作者及机构信息

1.
中南大学物理科学与技术学院超微结构和超快过程研究所,长沙 410083

基金项目: 中国博士后科学基金(批准号:20080431025),湖南省自然科学基金(批准号:08JJ3005)和中南大学博士后科学基金(批准号: 20071025) 资助的课题.

Authors and contacts

1.
Institute of Super Microstructure and Ultrafast Process, College of Physics Science and Technology, Central South University, Changsha 410083, China

参考文献

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[3]	Adleman L M 1994 Science 266 1021
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[21]	Adessi Ch, Walch S, Anantram M P 2003 Phys. Rev. B 67 081405
[22]	Yoo K H, Ha D H, Lee J O, Park J W, Kim J, Kim J J, Lee H Y, Kawai T, Choi H Y 2001 Phys. Rev. Lett. 87 198102
[23]	Bruinsma R, Grüner G, D'Orsogna M R, Rudnick J 2000 Phys. Rev. Lett. 85 4393
[24]	Berlin Y A, Burin A L, Rather M A 2000 J. Phys. Chem. A 104 443
[25]	Carpena P, B-Galván P, Ivanov P Ch, Stanley H E 2002 Nature 418 955
[26]	Albuquerque E L, Vasconcelos M S, Lyra M L, de Moura F A B F 2005 Phys. Rev. E 71 021910
[27]	de Moura F A B F, Lyra M L 1998 Phys. Rev. Lett. 81 3735
[28]	Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[29]	Peng C K, Buldyrev S V, Goldberger A L 1992 Nature 356 168
[30]	Liu X L, Huang X M, Xu H, Ren Y 2010 Acta Phys. Sin. 59 4202 (in Chinese) [刘小良、黄晓梅、徐慧、任意 2010 59 4202]
[31]	Farchioni R, Grosso G 1992 Phys. Rev. B 45 6383
[32]	Liu X L, Xu H, Deng C S, Ma S S 2007 Physica B 392 107
[33]	Anderson P W 1958 Phys. Rev. 109 1492
[34]	Liu X L, Ren Y, Xie Q T, Xu H 2010 Phys. Lett. A 374 2163
[35]	Sugiyama H, Saito I 1996 J. Am. Chem. Soc. 118 7063
[36]	Hurst H E, Black R, Sinaika Y M 1965 Long-Term Storage in Reservior: An Experimental Study (London: Constable)
[37]	Guo A M, Xiong S J 2009 Phys. Rev. B 80 035115
[38]	Xiong S J, Xiong Y 1999 Phys. Rev. Lett. 83 1407
[39]	Maciá E, Domínguez-Adame F, Sáchez A 1994 Phys. Rev. B 49 9503

施引文献

[1]	Eley D D, Spivey D I 1962 Trans. Faraday Soc. 58 411
[2]	Schena M, Shalon D, Davis R W, Brown P O 1995 Science 270 467
[3]	Adleman L M 1994 Science 266 1021
[4]	Mao C D, Sun W Q, Shen Z Y, Seeman N C 1999 Nature 397 144
[5]	Yurke B, Turberfield A J, Mills A P, Simmel F C, Neumann J L 2000 Nature 406 605
[6]	Fink H W, Schonenberger C 1999 Nature 398 407
[7]	Zhang W, Ulloa S E 2006 Phys. Rev. B 74 115304
[8]	Meng X L, Gao X T, Qu Z, Kang D W, Liu D S, Xie S J 2008 Acta Phys. Sin. 57 5316 (in Chinese) [孟宪兰、高绪团、渠朕、康大伟、刘德胜、解士杰 2008 57 5316]
[9]	Liu X L, Xu H, Ma S S, Deng C S Guo A M 2006 Acta Phys. Sin. 55 5562 (in Chinese) [刘小良、徐慧、马松山、邓超生、郭爱敏 2006 55 5562]
[10]	Zhang W, Yang R, Ulloa S E 2009 Phys. Rev. E 80 051901
[11]	Stephan R, Dominique B, Enrique M, Kats E 2003 Phys. Rev. Lett. 91 228101
[12]	Ma S S, Xu H, Wang H Y, Guo R 2009 Chin. Phys. B 18 3591
[13]	Gao J, Xu Z Y 2009 Chin. Phys. B 18 0370
[14]	Hartshom R M, Barton J K 1992 J. Am. Chem. Soc. 114 5919
[15]	Porath D, Bezryadin A, de Vries S, Dekker C 2000 Nature 403 635
[16]	Storm A J, van Noort J, de Vries S, Dekker C 2001 Appl. Phys. Lett. 79 3881
[17]	Zhang Y, Austin R H, Kraeft J, Cox E C, Ong N P 2002 Phys. Rev. Lett. 89 198102
[18]	Cuniberti G, Craco L, Porath D, Dekker C 2002 Phys. Rev. B 65 241314
[19]	Hjort M, Stafstrom S 2001 Phys. Rev. Lett. 87 228101
[20]	Kasumov A Y, Kociak M, Guéron S,Reulet B, Volkov V T, Klinov D V, Bouchiat H 2001 Science 291 280
[21]	Adessi Ch, Walch S, Anantram M P 2003 Phys. Rev. B 67 081405
[22]	Yoo K H, Ha D H, Lee J O, Park J W, Kim J, Kim J J, Lee H Y, Kawai T, Choi H Y 2001 Phys. Rev. Lett. 87 198102
[23]	Bruinsma R, Grüner G, D'Orsogna M R, Rudnick J 2000 Phys. Rev. Lett. 85 4393
[24]	Berlin Y A, Burin A L, Rather M A 2000 J. Phys. Chem. A 104 443
[25]	Carpena P, B-Galván P, Ivanov P Ch, Stanley H E 2002 Nature 418 955
[26]	Albuquerque E L, Vasconcelos M S, Lyra M L, de Moura F A B F 2005 Phys. Rev. E 71 021910
[27]	de Moura F A B F, Lyra M L 1998 Phys. Rev. Lett. 81 3735
[28]	Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[29]	Peng C K, Buldyrev S V, Goldberger A L 1992 Nature 356 168
[30]	Liu X L, Huang X M, Xu H, Ren Y 2010 Acta Phys. Sin. 59 4202 (in Chinese) [刘小良、黄晓梅、徐慧、任意 2010 59 4202]
[31]	Farchioni R, Grosso G 1992 Phys. Rev. B 45 6383
[32]	Liu X L, Xu H, Deng C S, Ma S S 2007 Physica B 392 107
[33]	Anderson P W 1958 Phys. Rev. 109 1492
[34]	Liu X L, Ren Y, Xie Q T, Xu H 2010 Phys. Lett. A 374 2163
[35]	Sugiyama H, Saito I 1996 J. Am. Chem. Soc. 118 7063
[36]	Hurst H E, Black R, Sinaika Y M 1965 Long-Term Storage in Reservior: An Experimental Study (London: Constable)
[37]	Guo A M, Xiong S J 2009 Phys. Rev. B 80 035115
[38]	Xiong S J, Xiong Y 1999 Phys. Rev. Lett. 83 1407
[39]	Maciá E, Domínguez-Adame F, Sáchez A 1994 Phys. Rev. B 49 9503

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