Semiclassical approximation for transmission through open Sinai billiards

doi:10.1088/1674-1056/22/2/020501

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (2): 20501-020501.doi: 10.1088/1674-1056/22/2/020501

Semiclassical approximation for transmission through open Sinai billiards

蔡祥吉^a, 张延惠^a, 李宗良^a, 蒋国辉^a, 杨秦男^a, 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

收稿日期:2012-04-12 修回日期:2012-07-18 出版日期:2013-01-01 发布日期:2013-01-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10804064 and 10774093).

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

Received:2012-04-12 Revised:2012-07-18 Online:2013-01-01 Published:2013-01-01
Contact: Zhang Yan-Hui E-mail:yhzhang@sdnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10804064 and 10774093).

摘要/Abstract

摘要： 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.

关键词: Sinai billiards, transmission amplitude, classical trajectories, power spectrum

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.

Key words: Sinai billiards, transmission amplitude, classical trajectories, power spectrum

中图分类号: (Quantum chaos; semiclassical methods)

05.45.Mt

73.23.Ad (Ballistic transport) 03.65.Sq (Semiclassical theories and applications)

蔡祥吉, 张延惠, 李宗良, 蒋国辉, 杨秦男, 徐学友. Semiclassical approximation for transmission through open Sinai billiards[J]. Chin. Phys. B, 2013, 22(2): 20501-020501.

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[J]. Chin. Phys. B, 2013, 22(2): 20501-020501.

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Semiclassical approximation for transmission through open Sinai billiards

Semiclassical approximation for transmission through open Sinai billiards

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