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arXiv 1406.7232cond-mat.mes-hall
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电荷脉冲的经典和量子扩展

Classical and quantum spreading of a charge pulse

Benoit Gaury, Joseph Weston, Christoph Groth, Xavier Waintal

摘要:

随着射频装置技术的进步,高频量子输运实验已经从理论走向实验室。到目前为止,用于处理这些问题的标准理论方法数值-称为Keldysh或NEGF(非平衡格林函数)形式主义-还没有很成功,主要是因为一个令人望而却步的计算成本。我们提出了一个非平衡格林函数技术的电子波函数的系统中的能量-时间表示。我们得到的数值算法现在与模拟的时间和系统的体积成线性关系,并且使得模拟具有10^5 - 10^6个原子/位置的系统是可行的。我们说明我们的方法与传播和传播的电荷脉冲在量子霍尔制度。我们确定了一个经典的和一个量子政权的传播,这取决于脉冲中包含的粒子的数量。这个数值实验是对量子力学教科书中讨论的高斯波包扩散的凝聚态模拟。

英文摘要:

With the technical progress of radio-frequency setups, high frequency quantum transport experiments have moved from theory to the lab. So far the standard theoretical approach used to treat such problems numerically--known as Keldysh or NEGF (Non Equilibrium Green's Functions) formalism--has not been very successful mainly because of a prohibitive computational cost. We propose a reformulation of the non-equilibrium Green's function technique in terms of the electronic wave functions of the system in an energy-time representation. The numerical algorithm we obtain scales now linearly with the simulated time and the volume of the system, and makes simulation of systems with 10^5 - 10^6 atoms/sites feasible. We illustrate our method with the propagation and spreading of a charge pulse in the quantum Hall regime. We identify a classical and a quantum regime for the spreading, depending on the number of particles contained in the pulse. This numerical experiment is the condensed matter analogue to the spreading of a Gaussian wavepacket discussed in quantum mechanics textbooks.

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