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arXiv 1204.6490cond-mat.dis-nnmath-phmath.MP
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磁场作用下无序系统的量子输运:基于算子代数的研究

Quantum transport in disordered systems under magnetic fields: A study based on operator algebras

Emil Prodan

摘要:

一般均匀微观量子模型的线性电导率张量在文献[1]中被表述为非对易的Kubo公式。\cite{BELLISSARD:1994xj,Schulz-Baldes:1998vm,Schulz-Baldes:1998oq}。这个公式是直接在热力学极限下,在$C^*$ -代数和定义在无限空间上的非交换演算的框架内导出的。因此,形式主义的数字实施遇到了根本性的障碍。目前的工作定义了一个$C^*$ -代数和一个近似的非交换微积分上的有限实空间环面,这自然会导致一个近似的有限体积的非交换久保公式,在计算机上进行。对于有限的温度和耗散,它表明,这个近似公式指数快速收敛到它的热力学极限,这是确切的非交换久保公式。近似的非对易Kubo公式,然后解构的形式,是在计算机上实现和模拟的量子输运在一个磁场中的二维无序格子气。

英文摘要:

The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. \cite{BELLISSARD:1994xj,Schulz-Baldes:1998vm,Schulz-Baldes:1998oq}. This formula was derived directly in the thermodynamic limit, within the framework of $C^*$-algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a $C^*$-algebra and an approximate noncommutative calculus over a finite real-space torus, which naturally leads to an approximate finite-volume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a 2-dimensional disordered lattice gas in a magnetic field are presented.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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