Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(1): 018708    DOI: 10.1088/1674-1056/25/1/018708

Quantum dynamics of charge transfer on the one-dimensional lattice: Wave packet spreading and recurrence

V N Likhachev, O I Shevaleevskii, G A Vinogradov
Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, Russian Federation

The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site (donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ~ t1/3 and its amplitude decreases ~ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.

Keywords:  quantum dynamics      tight-binding approximation      charge transport     
Received:  01 April 2015      Published:  05 January 2016
PACS:  87.15.-v (Biomolecules: structure and physical properties)  
  42.15.Dp (Wave fronts and ray tracing)  
Corresponding Authors:  G A Vinogradov     E-mail:

Cite this article: 

V N Likhachev, O I Shevaleevskii, G A Vinogradov Quantum dynamics of charge transfer on the one-dimensional lattice: Wave packet spreading and recurrence 2016 Chin. Phys. B 25 018708

[1] Eberhard S, Finazzi G and Wollmann F A 2008 Annu. Rev. Genet. 42 463
[2] Burda K 2007 Cell Biochem. Biophys. 47 271
[3] Ferreira K N, Iverson T M, Maghlaoui K, Barber J and Iwata S 2004 Science 303 1831
[4] Loll B, Kern J, Saenger W, Zouni A and Biesiadka J 2005 Nature 438 1040
[5] Rich P R 2003 Biochem. Soc. Trans. 31 1095
[6] Verkhovskaya M L, Belevich N, Euro L, Wikström M and Verkhofsky M 2008 Proc. Natl. Acad. Sci. USA 105 3763
[7] Augustyn K E, Genereux J C and Barton J K 2007 Angew. Chem. Int. Ed. 46 5731
[8] Barton J K, Olmon E D and Sontz P A 2011 Coord. Chem. Rev. 255 619
[9] Genereux J C and Barton J K 2010 Chem. Rev. 110 1642
[10] Mallajosyula S S and Pati S K 2010 J. Phys. Chem. Lett. 1 1881
[11] Giese B 2002 Annu. Rev. Biochem. 71 51
[12] Slater C and Koster G F 1954 Phys. Rev. 94 1498
[13] Anderson P W 1958 Phys. Rev. 109 1492
[14] Biswas P, Cain P, Römer R A and Schreiber M 2000 arXiv:cond-mat/0001315[cond-mat.dis-nn]
[15] Kantelhardt J W, Berkovits R, Havlin S and Bunde A 1999 Physica A 266 461
[16] Kohmoto M, Sutherland B and Tang C 1987 Phys. Rev. B 35 1020
[17] Ludlam J J, Taraskin S N and Elliott S R 2003 Phys. Rev. B 67 122203
[18] Milde F, Römer R A and Schreiber M 1997 Phys. Rev. B 55 9463
[19] Flach S 2010 Chem. Phys. 375 548
[20] de Moura F A B F, Caetano R A and Santos B 2012 J. Phys.: Condens. Matter 24 245401
[21] Evangelou S N and Pichard J L 2000 Phys. Rev. Lett. 84 1643
[22] Ng G S and Kottos T 2007 Phys. Rev. B 75 205120
[23] Ketzmerick R, Kruse K, Kraut S and Geisel T 1997 Phys. Rev. Lett. 79 1959
[24] Zhong J, Diener R B, Steck D A, Oskay W H, Raizen M G, Plummer E W, Zhang Z and Niu Q 2001 Phys. Rev. Lett. 86 2485
[25] Fermi E, Pasta J and Ulam S 1955 Los Alamos report LA-1940 (reprinted in Collected Papers of Enrico Fermi, Segre E ed., Vol. II, 1965, University of Chicago Press, p. 978)
[26] Berman G P and Izrailev F M 2005 Chaos 15 015104
[27] Ovchinnikov A A, Erikhman N S and Pronin K A 2001 Vibrational-Rotational Excitations in Nonlinear Molecular Systems (New York: Kluwer Acedemic/Plenum Publishers) p. 298
[28] Zwanzig R 1960 Lect. Theor. Phys. 3 106
[29] Benderskii V A, Falkovsky L A and Kats E I 2007 JETP Lett. 86 221
[30] Likhachev V N, Astakhova T Y and Vinogradov G A 2014 Theor. Math. Physics 180 1086
[31] Benderskii V A, Kotkin A S, Rubtsov I V and Kats E I 2013 JETP Lett. 98 219
[32] Benderskii V A and Kats E I 2011 JETP Lett. 94 459
[33] Ndawana M L, Römer R A and Schreiber M 2002 Eur. Phys. J. B 27 399
[34] Deych L I, Lisyansky A A and Altshuler B L 2001 Phys. Rev. B 64 224202
[35] MacKinnon A and Kramer B 1983 Z. Phys. B-Condens. Matter 53 1
[36] MacKinnon A 1994 J. Phys.: Condens. Matter 6 2511
[37] Pichard J L and Sarma G 1981 J. Phys. C: Solid State Phys. 14 L127
[38] Pichard J L and Sarma G 1981 J. Phys. C: Solid State Phys. 14 L617
[39] Elias B, Genereux J C and Barton J K 2008 Angew. Chem. Int. Ed. 47 9067
[40] Gradstein I S and Ryzhik I M 2007 Table of Integrals, Series, and Products (7th edn.) (Amsterdam: Elsevier)
[41] Hufnagel L, Ketzmerick R, Kottos T and Geisel T 2001 Phys. Rev. E 64 012301
[42] Zhang Z, Tong P, Gong J and Li B 2012 Phys. Rev. Lett. 108 070603
[43] Conwell E M and Rakhmanova S V 2000 Proc. Natl. Acad. Sci. USA 97 4556
[44] Rakhmanova S V and Conwell E M 2001 J. Phys. Chem. B 105 2056
[45] Conwell E M and Basko D M 2001 J. Am. Chem. Soc. 123 11441
[46] Conwell E M, Park J H and Choi H Y 2005 J. Phys. Chem. B 109 9760
[47] Conwell E M, McLaughlin P M and Bloch S M 2008 J. Phys. Chem. B 112 2268
[48] Zhang G, Hu H, Cui S and Lv Z 2010 Physica B 405 4382
[49] Zhang G, Cui P, Wu J and Liu C 2009 Physica B 404 1485
[50] Wei J H, Liu X J, Berakdar J and Yan Y 2008 J. Chem. Phys. 128 165101
[51] Chakrabarti B, Piette B M A G and Zakrzewski W J 2012 EPL 97 47005
[1] Reaction mechanism of D+ND→N+D2 and its state-to-state quantum dynamics
Ting Xu(许婷), Juan Zhao(赵娟), Xian-Long Wang(王宪龙), Qing-Tian Meng(孟庆田). Chin. Phys. B, 2019, 28(2): 023102.
[2] Novel potential energy surface-based quantum dynamics of ion-molecule reaction O++D2 →OD++D
Xian-Long Wang(王宪龙), Feng Gao(高峰), Shou-Bao Gao(高守宝), Lu-Lu Zhang(张路路), Yu-Zhi Song(宋玉志), Qing-Tian Meng(孟庆田). Chin. Phys. B, 2018, 27(4): 043104.
[3] State-to-state dynamics of F(2P)+HO(2Π) →O(3P)+HF(1+) reaction on 13A" potential energy surface
Juan Zhao(赵娟), Hui Wu(吴慧), Hai-Bo Sun(孙海波), Li-Fei Wang(王立飞). Chin. Phys. B, 2018, 27(2): 023102.
[4] Phase transition and charge transport through a triple dot device beyond the Kondo regime
Yong-Chen Xiong(熊永臣), Zhan-Wu Zhu(朱占武), Ze-Dong He(贺泽东). Chin. Phys. B, 2018, 27(10): 108503.
[5] Coherent charge transport in ferromagnet/semiconductor nanowire/ferromagnet double barrier junctions with the interplay of Rashba spin–orbit coupling, induced superconducting pair potential, and external magnetic field
Li-Jie Huang(黄立捷), Lian Liu(刘恋), Rui-Qiang Wang(王瑞强), Liang-Bin Hu(胡梁宾). Chin. Phys. B, 2017, 26(7): 077201.
[6] A simulation study on p-doping level of polymer host material in P3HT: PCBM bulk heterojunction solar cells
Hossein Movla, Mohammad Babazadeh. Chin. Phys. B, 2017, 26(4): 048802.
[7] Study of a ternary blend system for bulk heterojunction thin film solar cells
Zubair Ahmad, Farid Touati, Shakoor R A, Al-Thani N J. Chin. Phys. B, 2016, 25(8): 080701.
[8] Electronic mobility in the high-carrier-density limit ofion gel gated IDTBT thin film transistors
Bao Bei, Shao Xian-Yi, Tan Lu, Wang Wen-He, Wu Yue-Shen, Wen Li-Bin, Zhao Jia-Qing, Tang Wei, Zhang Wei-Min, Guo Xiao-Jun, Wang Shun, Liu Ying. Chin. Phys. B, 2015, 24(9): 098103.
[9] State-to-state quantum dynamics of the N(4S)+H2 (X1Σ+)→NH(X3-)+H(2S) reaction and its reaction mechanism analysis
Zhang Jing, Gao Shou-Bao, Wu Hui, Meng Qing-Tian. Chin. Phys. B, 2015, 24(8): 083104.
[10] A typical slow reaction H(2S)+S2(X3Σg-)→SH(X2∏)+S(3P) on a new surface:Quantum dynamics calculations
Wei Wei, Gao Shou-Bao, Sun Zhao-Peng, Song Yu-Zhi, Meng Qing-Tian. Chin. Phys. B, 2014, 23(7): 073101.
[11] Resonant tunneling through double-barrier structures on graphene
Deng Wei-Yin, Zhu Rui, Xiao Yun-Chang, Deng Wen-Ji. Chin. Phys. B, 2014, 23(1): 017202.
[12] Quantum dynamic behaviour in a coupled cavities system
Peng Jun, Wu Yun-Wen, Li Xiao-Juan. Chin. Phys. B, 2012, 21(6): 060302.
[13] Charging dynamics of polymer due to electron irradiation: A simultaneous scattering-transport model and preliminary results
Cao Meng, Wang Fang, Liu Jing, Zhang Hai-Bo. Chin. Phys. B, 2012, 21(12): 127901.
No Suggested Reading articles found!