Semiclassical approximation for transmission through open Sinai billiards

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

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

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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

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Semiclassical approximation for transmission through open Sinai billiards

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