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arXiv 0909.3295cond-mat.mes-hallnlin.CDnucl-th
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弹道量子点中相互作用矩阵元涨落的动力学效应

Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Dynamical Effects

L. Kaplan, Y. Alhassid

摘要:

我们研究了两体屏蔽库仑相互作用和弹道量子点中的单体表面电荷势的矩阵元波动,将实际混沌台球中的行为与以前在归一化随机波模型中获得的分析结果进行比较。我们发现,在实际的混沌台球的矩阵元素的方差通常超过了3或4的随机波模型的预测的一个因素,在实验中常用的点的大小。我们讨论的动力学效应,负责这种增强。这些动力学效应对协方差的影响更为显著,与随机波浪预测相比,协方差改变了符号。在台球,不显示硬混沌,甚至更大的增强矩阵元素的波动是可能的。这些增强的波动的峰值间距统计和光谱混乱的量子点在库仑阻塞制度的影响。

英文摘要:

We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously obtained in a normalized random wave model. We find that the matrix element variances in actual chaotic billiards typically exceed by a factor of 3 or 4 the predictions of the random wave model, for dot sizes commonly used in experiments. We discuss dynamical effects that are responsible for this enhancement. These dynamical effects have an even more striking effect on the covariance, which changes sign when compared with random wave predictions. In billiards that do not display hard chaos, an even larger enhancement of matrix element fluctuations is possible. These enhanced fluctuations have implications for peak spacing statistics and spectral scrambling for quantum dots in the Coulomb blockade regime.

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