Scattering Theory and Non-Equilibrium Transport in Quantum

该奖项支持在非平衡强相关纳米结构动力学方面的理论研究和教育。该项目将有助于我们理解如何描述由保持在不同化学势或温度下的引线施加电流的相互作用量子系统，这是一个具有重要实际应用的理论和实验基础重要性的主题。该研究结合了几个主题领域：强相关电子系统的研究，旨在理解相互作用带来的新的集体现象；纳米结构的研究涉及在受限几何中分析输运和光谱性质的问题，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。所有这些领域都为纳米器件的动力学研究提供了必不可少的组成部分。制造技术的进步使得纳米器件可以进行实验。因此，非平衡物理的基本问题可以用高精度的实验来检验。这需要PI旨在提供的详细的理论预测。所追求的理论方法是基于散射理论，散射本征态通过贝特安萨兹构造。特征态定义在开无限线上，边界条件由引线施加的偏置电压或温度降设定。人们得到了非平衡性质的明确预测，如电荷和热流，熵的产生和耗散，以及介观中的中心量，如退相干时间和弛豫速率。所有这些量都可以通过实验来检验。PI将把这种方法应用于非平衡系统的具体模型，包括：两导联安德森模型用于模拟量子点，两导联霍尔斯坦模型用于模拟断结中的分子，以及两导联AB干涉仪。PI的目标是发展精确的预测，可以与实验进行比较，并可能导致对稳态行为的新见解。该项目有助于培养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。PI目前也在写一本关于量子杂质系统的非微扰方法的书。该奖项支持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10到100倍的原子系统中相互强烈作用。PI将关注这些纳米结构中的电子不处于平衡和平静状态的情况。相反，PI将研究电子远离平衡的情况，如在纳米结构上施加电压迫使电子移动时可能发生的情况。远离平衡的系统没有得到很好的理解。由于它们之间的强相互作用而产生的电子的相关运动提供了额外的复杂性，但为了开发理论和概念工具，使建模和设计可能在纳米尺度上开发的必要的量子力学电子设备成为可能，这是一个重要的因素。博士后和学生研究人员将参与这项研究，这将有助于他们在先进理论技术方面的教育，以及这些技术在纳米尺度上材料和设备模糊界面的材料和系统中的应用。

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.