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arXiv 0712.4095cond-mat.mes-hallcond-mat.str-elnlin.CD
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量子点中的相互作用矩阵元涨落

Interaction matrix element fluctuations in quantum dots

L. Kaplan

摘要:

在弹道量子点的库仑阻塞机制中,众所周知,电导峰间距的分布被单粒子图像错误地预测;相反,需要考虑剩余电子相互作用的矩阵元素波动。在规范化的随机波模型,有效的半经典极限的电子数的点变得很大,我们得到的两体和一体矩阵元的波动的解析表达式。然而,这些波动可能太小,无法解释低温实验数据。我们已经研究了矩阵元素的波动在现实的混沌几何形状,并表明,在能量的实验兴趣,这些波动一般超过约3-4的随机波模型的预测的一个因素。甚至更大的波动发生在具有混合混沌-规则相空间的几何中。这些结果可以允许Hartree-Fock图片和实验之间更好的协议。在其他研究结果中,我们表明,相互作用矩阵元素的分布是强烈的非高斯的参数范围内的实验兴趣,即使在随机波模型。我们还发现,在现实的几何形状中的增强的波动不能使用领先的顺序半经典的方法计算,但可以理解的短期动力学。

英文摘要:

In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic interaction need to be taken into account. In the normalized random-wave model, valid in the semiclassical limit where the number of electrons in the dot becomes large, we obtain analytic expressions for the fluctuations of two-body and one-body matrix elements. However, these fluctuations may be too small to explain low-temperature experimental data. We have examined matrix element fluctuations in realistic chaotic geometries, and shown that at energies of experimental interest these fluctuations generically exceed by a factor of about 3-4 the predictions of the random wave model. Even larger fluctuations occur in geometries with a mixed chaotic-regular phase space. These results may allow for much better agreement between the Hartree-Fock picture and experiment. Among other findings, we show that the distribution of interaction matrix elements is strongly non-Gaussian in the parameter range of experimental interest, even in the random wave model. We also find that the enhanced fluctuations in realistic geometries cannot be computed using a leading-order semiclassical approach, but may be understood in terms of short-time dynamics.

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