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Chin. Phys. B, 2013, Vol. 22(2): 020501    DOI: 10.1088/1674-1056/22/2/020501
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Semiclassical approximation for transmission through open Sinai billiards

Cai Xiang-Ji (蔡祥吉)a, Zhang Yan-Hui (张延惠)a, Li Zong-Liang (李宗良)a, Jiang Guo-Hui (蒋国辉)a, Yang Qin-Nan (杨秦男)a, Xu Xue-You (徐学友)b
a College of Physics and Electronics, Shandong Normal University, Jinan 250014, China;
b Information Research Institute, Shandong Academy of Sciences, Jinan 250014, China
Abstract  We use a semiclassical approximation to study the transport through the weakly open chaotic Sinai quantum billiards which can be considered as the schematic of a Sinai mesoscopic device, with the diffractive scatterings at the lead openings taken into account. The conductance of the ballistic microstructure which displays universal fluctuations due to quantum interference of electrons can be calculated by Landauer formula as a function of the electron Fermi wave number, and the transmission amplitude can be expressed as the sum over all classical paths connecting the entrance and the exit leads. For the Sinai billiards, the path sum leads to an excellent numerical agreement between the peak positions of power spectrum of the transmission amplitude and the corresponding lengths of the classical trajectories, which demonstrates a good agreement between the quantum theory and the semiclassical theory.
Keywords:  Sinai billiards      transmission amplitude      classical trajectories      power spectrum  
Received:  12 April 2012      Revised:  18 July 2012      Accepted manuscript online: 
PACS:  05.45.Mt (Quantum chaos; semiclassical methods)  
  73.23.Ad (Ballistic transport)  
  03.65.Sq (Semiclassical theories and applications)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10804064 and 10774093).
Corresponding Authors:  Zhang Yan-Hui     E-mail:  yhzhang@sdnu.edu.cn

Cite this article: 

Cai Xiang-Ji (蔡祥吉), Zhang Yan-Hui (张延惠), Li Zong-Liang (李宗良), Jiang Guo-Hui (蒋国辉), Yang Qin-Nan (杨秦男), Xu Xue-You (徐学友) Semiclassical approximation for transmission through open Sinai billiards 2013 Chin. Phys. B 22 020501

[1] Sohn L L 1998 Nature 394 131
[2] Ferry D K, Goodnick S M and Bird J 2009 Transport in Nanostructures 2nd edn. (Cambridge: Cambridge University Press) p. 2
[3] Datto S 1995 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press) p. 1
[4] Richter K 2000 Semiclassical Theory of Mesoscopic Quantum Systems (New York: Springer-Verlag) p. 1
[5] Heinzel T 2007 Mesoscopic Electronics in Solid State Nanostructures 2nd edn. (KGaA: WILEY-VCH Verlag GmbH & Co.) p. 2
[6] Ihn T 2010 Semiconductor Nanostructures Quantum States and Electronic Transport (Oxford: Oxford University Press) p. 95
[7] Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer-Verlag) p. 3
[8] Du M L and Delos J B 1987 Phys. Rev. Lett. 58 1731
[9] Du M L and Delos J B 1988 Phys. Rev. A 38 1896
[10] Lu J and Du M L 2004 Acta Phys. Sin. 53 2450 (in Chinese)
[11] Xu X Y, Zhang Y H, Huang F Z, Lin S L and Du M L 2005 Acta Phys. Sin. 54 4538 (in Chinese)
[12] Zhang Y H, Zhang L Q, Xu X Y, Ge M H, Lin S L and Du M L 2006 Chin. Phys. 15 502
[13] Zhang Y H, Zhang J Q, Xu X Y and Lin S L 2009 Chin. Phys. B 18 35
[14] Zhang J Q, Zhang Y H, Zhou H, Jia Z M and Lin S L 2009 Acta Phys. Sin. 58 5965 (in Chinese)
[15] Schwieters C D, Alford J A and Delos J B 1996 Phys. Rev. B 54 10652
[16] Wirtz L, Tang J Z and Burgdörfer J 1997 Phys. Rev. B 56 7589
[17] Wirtz L, Stampfer C, Rotter S and Burgdörfer J 2003 Phys. Rev. E 67 016206
[18] Stampfer C, Rotter S and Burgdörfer J 2005 Phys. Rev. E 72 036223
[19] Brack M and Bhaduri R K 1997 Semiclassical Physics (Reading Mass: Addison-Wesley Publishing Company) p. 1
[20] Nazmitdinov R G, Pichugin K N, Rotter I and Šeba P 2002 Phys. Rev. B 66 085322
[21] Sohn L L, Kouwenhoven L P and Schön G 1997 Mesoscopic Electron Transport (Boston: Kluwer Academic Publishers) p. 106
[22] Berry M V and Mount K E 1972 Rep. Prog. Phys. 35 315
[23] Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York: MacGraw-Hill) p. 31
[24] Berry M J, Baskey J H, Westervelt R M and Gossard A C 1994 Phys. Rev. B 50 8857
[25] Landauer R 1957 IBM J. Res. Dev. 1 223
[26] Xu X Y, Wang S B, Jia Z M and Lin S L 2007 J. At. Mol. Phys. 5 999 (in Chinese)
[27] Xu X Y, Zhang Y H, Li H Y, Gao S and Lin S L 2008 Chin. Phys. Lett. 25 1549
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