Scattering Theory and Non-Equilibrium Transport in Quantum

技术总结该奖项支持关于强关联纳米结构失去平衡的动力学的理论研究和教育。该项目将有助于我们理解如何描述相互作用的量子系统，该系统携带由保持在不同化学势或温度下的铅施加的电流，这是一个具有重大实际应用的理论和实验的基本重要课题。这项研究结合了几个主题领域：研究强关联电子系统，试图了解相互作用带来的新的集体现象；研究纳米结构，涉及在受限几何中分析的输运和光谱性质问题，重点是无序和相互作用之间的相互作用；多体量子系统中的非平衡热力学。所有这些领域都为研究纳米级设备的动力学提供了必不可少的组成部分。制造技术的进步使纳米设备可以进行实验。因此，非平衡物理的基本问题可以在实验上得到高度精确的测试。这需要PI旨在提供的详细理论预测。所追求的理论方法是基于散射理论，通过Bethe Ansat构造散射本征态。本征态定义在开放的无限长线上，边界条件由导线施加的偏置电压或温降设置。人们得到了对非平衡性质的明确预测，如电荷和热流、熵产生和耗散，以及介观中的中心量，如消相干时间和弛豫速率。PI将把这种方法应用到非平衡系统的具体模型中，包括：双导Anderson模型模拟量子点，双导Holstein模型模拟断裂结中的分子，以及双导AB干涉仪。PI旨在开发可以与实验相比较的精确预测，并可能导致对稳态行为的新见解。该项目有助于博士后和学生研究人员学习先进的理论技术，并将其应用于具体的实验系统。国际和平研究所目前还在写一本关于量子杂质系统的非微扰方法的书。非技术总结该奖项支持关于电子动力学的理论研究和教育，这些电子在比人类头发直径小十到一百倍的原子系统中相互作用强烈。PI将专注于这些纳米结构中的电子不处于平衡和平静的平衡状态的情况。相反，PI将调查电子远离平衡的情况，当在纳米结构上施加电压迫使电子移动时可能会发生这种情况。远离均衡的系统并没有得到很好的理解。电子的强相互作用产生的相互关联的运动提供了额外的复杂性，但为了开发能够对可能在纳米尺度上开发的必要的量子力学电子设备进行建模和设计的理论和概念工具，这是一个重要的组成部分。博士后和学生研究人员将参与这项研究，这将有助于他们进行先进理论技术的教育，并将这些技术应用于纳米尺度上材料和设备的模糊界面上的材料和系统。

TECHNICAL SUMMARYThis award supports theoretical research and education on dynamics of strongly correlated nanostructures out of equilibrium. The project will contribute to our understanding of how to describe interacting quantum systems carrying currents imposed by leads kept at different chemical potentials or temperatures, a subject of fundamental importance for theory and experiment with significant practical applications. The research combines several topical areas: the study of strongly correlated electron systems which seeks to understand new collective phenomena brought about by interactions; the study of nanostructures involving problems of transport and spectral properties analyzed in restricted geometries with emphasis on the interplay between disorder and interactions; nonequilibrium thermodynamics in many-body quantum systems. All these areas provide essential components in the study of the dynamics in nanoscale devices. Advances in fabrication have made nanodevices accessible to experiment. So, fundamental issues of nonequilibrium physics can be tested experimentally with a high degree of precision. This requires detailed theoretical predictions that the PI aims to provide. The theoretical approach to be pursued is based on scattering theory with the scattering eigenstates constructed via the Bethe Ansatz. The eigenstates are defined on the open infinite line with boundary conditions set by the bias voltage or temperature drop imposed by the leads. One obtains explicit predictions for non-equilibrium properties, such as charge and heat currents, entropy production and dissipation, as well as for quantities central in mesoscopics such as decoherence times and relaxation rates. All of these quantities can be experimentally tested.The PI will apply this approach to concrete models of nonequilibrium systems, including: the two leads Anderson model to model a quantum dot, the two leads Holstein model to model molecules in break junctions, and the two leads AB interferometer. The PI aims to develop precise predictions that can be compared with experiment and may lead to new insights about steady-state behaviors. This project contributes to the education of postdocs and student researchers in learning advanced theoretical techniques and their application to concrete experimental systems. The PI is also currently writing a book on nonperturbative approaches to quantum impurity systems.NONTECHNICAL SUMMARYThis award supports theoretical research and education on dynamics of electrons which interact strongly with each other in systems of atoms that are some ten to hundred times smaller than the diameter of a human hair. The PI will focus on situations where the electrons in these nanostructures are not in the balanced and tranquil state of equilibrium. Rather, the PI will investigate situations where the electrons are far from equilibrium as might happen when a voltage is applied across a nanostructure forcing the electrons to move. Systems far from equilibrium are not well understood. The correlated motion of electrons that results from their strong interaction provides additional complexity, but is an important ingredient to include in order to develop the theoretical and conceptual tools that enable the modeling and design of the necessarily quantum mechanical electronic devices that may be developed on the nanoscale. Postdocs and student researchers will be involved in the research, which will contribute to their education in advanced theoretical techniques and the application of these techniques to materials and systems at the blurry interface of materials and devices on the nanoscale.