非线性强度任意二聚的非线性链的透射性质

胡冬生; 张艳玲; 尹小刚; 徐江

doi:10.7498/aps.61.177103

摘要

用离散的非线性薛定谔的递推关系研究了非线性强度任意二聚的非线性链的透射性质. 结果表明该链存在一个共振透射态,共振态的能量为非线性强度与入射波振幅模平方的乘积; 取出射波振幅为定值和取入射波振幅模为定值来计算透射系数,其结果在非共振态有明显的差别: 取出射波振幅为定值时电子的透射随能量为单值函数,而取入射波振幅模为定值时电子的透射呈现多稳态. 并指出只有取入射波振幅模为定值时才能真正反映非线性强度对电子透射性质的影响.

关键词:

无序结构 /
退局域 /
多稳态

Abstract

By using the recursion relation of discrete Schrödinger equation we investigate the transport properties of nonlinear chains with random dimer nonlinearity parameters. It is shown that there is a resonance state, which is just the product of the nonlinearity and the square of the incident wave amplitude modulus. The transmission coefficients are calculated in two conditions. One is that the transmission wave amplitude is a certain value, the other is that the incident wave amplitude modulus is a certain value. There are obvious differences in non-resonant states between the two kinds of conditions. The transmission is a single value function of the electronic energy for the former. However, it will be multi-stability for the latter. It is pointed out that the influence of the nonlinearity parameters on the transport properties can be exactly reflected only when the modulus of incident wave is set to be a certain value.

Keywords:

作者及机构信息

1.
南京航空航天大学理学院, 南京 211100;

2.
南京航空航天大学材料科学与技术学院, 南京 211100

基金项目: 国家自然科学基金 (批准号: 51175245);江苏省自然科学基金(批准号: BK2010073)和南京航空航天大学基金(批准号: NS2010207)资助的课题.

Authors and contacts

1.
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China;

2.
Department of Material Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51175245), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010073), and NUAA research foundation (Grant No. NS2010207).

参考文献

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[17]	Hostein T 1959 Ann. Phys. (N. Y.) 8 325
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[19]	Hopkins V A, Keat J, Meegan G D, Zhang T M, Maynard J D 1996 Phys. Rev. Lett. 76 1102
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[22]	Cota E C, José J V, Maytorena J, Monsivais G 1995 Phys. Rev. Lett. 74 3302
[23]	Senouci K, Zekri N, Bahlouli H, Sen A K 1999 J. Phys.: Condens. Matter 11 1823
[24]	García-Mata I, Shepelyansky D L 2009 Phys. Rev. E 79 026205
[25]	Zhang Z J, Tong P Q, Gong J B, Li B W 2011 Phys. Rev. E 83 056205
[26]	Delyon F, Lévy Y E, Souillard B 1986 Phys. Rev. Lett. 57 2010
[27]	Cota E, José J V, Maytorena J, Monsivais G 1995 Phys. Rev. Lett. 74 3302
[28]	Shadrivov I V, Bliokh K Y, Bliokh Y P, Freilikher V, Kivshar Y S 2010 Phys. Rev. Lett. 104 123902
[29]	Datta P K 2007 Phys. Rev. B 75 205127
[30]	Senouci K 2007 J. Phys.: Condens. Matter 19 076202
[31]	Senouci K 2010 Physica B 405 694

施引文献

[1]	Anderson P W 1958 Phys. Rev. 109 1492
[2]	Abrahams E, Anderson P W, Licciardello D C, Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
[3]	Dunlap D, Wu H L, Philips P W 1990 Phys. Rev. Lett. 65 88
[4]	Xiong S J 1993 Appl. Phys. Lett. 63 81
[5]	Ojeda P, Huerta-Quintanilla R, Rodríguez-Achach M 2002 Phys. Rev. B 65 233102
[6]	Sedrakyan T 2004 Phys. Rev. B 69 085109
[7]	de Moura F A B F, Lyra M L 1998 Phys. Rev. Lett. 81 3735
[8]	Zhang G P, Xiong S J 2002 Eur. Phys. J. B 29 491
[9]	Kivshar Y S, Gredeskul S A, Sánchez A, Vásquez L 1990 Phys. Rev. Lett. 64 1693
[10]	Hu D S, Lu X J, Zhang Y M, Zhu C P 2009 Chin. Phys. B 18 2498
[11]	Hu D S, Zhu C P, Zhang Y M 2011 Chin. Phys. B 20 017104
[12]	Molina M I, Tsinoris G P 1994 Phys. Rev. Lett. 73 464
[13]	Kottos T, Weiss M 2004 Phys. Rev. Lett. 93 190604
[14]	Davids P S 1995 Phys. Rev. B 52 4146
[15]	Liu X L, Xu H, Ma S S, Song Z Q 2006 Acta Phys. Sin. 55 2949 (in Chinese) [刘小良, 徐慧, 马松山, 宋招权 2006 55 2949]
[16]	Bellani V, Diez E, Hey P, Toni L, Tarńcone L, Parravicini G B, Dominguez-Adame F, Gómez-Alcala R 1999 Phys. Rev. Lett. 82 2159
[17]	Hostein T 1959 Ann. Phys. (N. Y.) 8 325
[18]	Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353
[19]	Hopkins V A, Keat J, Meegan G D, Zhang T M, Maynard J D 1996 Phys. Rev. Lett. 76 1102
[20]	Molina M I 1998 Phys. Rev. B 58 12547
[21]	Senouci K, Zekri N 2000 Phys. Rev. B 62 2987
[22]	Cota E C, José J V, Maytorena J, Monsivais G 1995 Phys. Rev. Lett. 74 3302
[23]	Senouci K, Zekri N, Bahlouli H, Sen A K 1999 J. Phys.: Condens. Matter 11 1823
[24]	García-Mata I, Shepelyansky D L 2009 Phys. Rev. E 79 026205
[25]	Zhang Z J, Tong P Q, Gong J B, Li B W 2011 Phys. Rev. E 83 056205
[26]	Delyon F, Lévy Y E, Souillard B 1986 Phys. Rev. Lett. 57 2010
[27]	Cota E, José J V, Maytorena J, Monsivais G 1995 Phys. Rev. Lett. 74 3302
[28]	Shadrivov I V, Bliokh K Y, Bliokh Y P, Freilikher V, Kivshar Y S 2010 Phys. Rev. Lett. 104 123902
[29]	Datta P K 2007 Phys. Rev. B 75 205127
[30]	Senouci K 2007 J. Phys.: Condens. Matter 19 076202
[31]	Senouci K 2010 Physica B 405 694

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