Semiclassical approximation for transmission through open Sinai billiards

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 microstr...

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Published inChinese physics B Vol. 22; no. 2; pp. 128 - 132
Main Author 蔡祥吉 张延惠 李宗良 蒋国辉 杨秦男 徐学友
Format Journal Article
LanguageEnglish
Published 01.02.2013
Subjects
Amplitudes
Approximation
Chaos theory
Devices
Diffraction
Mathematical analysis
Mathematical models
Trajectories
半经典理论
半经典近似
台球
微观结构
数字传输
经典轨迹
西奈半岛
量子干涉
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/2/020501

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Summary: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.
Bibliography:Cai Xiang-Ji, Zhang Yan-Hui, Li Zong-Liang, Jiang Guo-Hui, Yang Qin-Nan, Xu Xue-You（ 1） College of Physics and Electronics, Shandong Normal University, Jinan 250014, China ;2） Information Research Institute, Shandong Academy of Sciences, Jinan 250014, China
Sinai billiards,transmission amplitude,classical trajectories,power spectrum
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.
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/2/020501