Scattering and Non-Equilbrium Transport in Quantum Importity Systems

非技术摘要这笔赠款支持涉及杂质对量子点和纳米电子学等系统性质的影响的理论研究。特别是，我们将研究这些系统在非平衡条件下的性质。过去的大部分工作都是关于均衡系统的。然而，在实际应用中，非平衡条件更为现实。该项目将涉及研究生和博士后研究人员的参与。技术摘要智力价值：非平衡量子杂质系统的研究处于介观和强关联物理的交叉点。最近在实验技术上的巨大进步使得在量子点等纳米器件中实现杂质模型成为可能，其中由于低维的原因，量子涨落大大增强。描述非均衡条件和强相关性之间的相互作用是一项艰巨的智力挑战。这一建议解决了非平衡稳态的问题，这是更普遍的问题的一个小角落。提出了一种新的概念框架，允许精确和显式地计算量子杂质模型的非平衡稳态性质。特别是，它允许计算许多实验上可测量的量，如通过点的电流和状态的非平衡杂质密度。该框架还允许精确计算量子杂质模型中的散射性质，因此对于解释金属导线中的退相干和反常能量弛豫等物理现象具有重要意义。广泛影响：非平衡现象在自然界中普遍存在，但相对较少被理解。这与一个多世纪前玻尔兹曼提供的普遍框架的均衡现象截然不同。在众多的非平衡现象中，稳态是最简单的。这项工作将打造概念和实用工具，为量子杂质模型中的稳态动力学提供准确的描述。在过去，精确解在增进我们对平衡统计力学的理解方面发挥了重要作用。因此，可望通过提供一组具有重要实验实现的模型的精确解，所提出的研究将有助于为非平衡稳态的一般公式指明方向。在更实际的层面上，拟议的研究将有助于澄清在温度和电压梯度下运行的纳米器件的适用范围。这对现代量子电子学具有直接的实际意义。将研究以下项目：非平衡量子杂质：提出了一个新的概念框架，它允许精确计算由非平衡Kondo或Anderson模型描述的量子点在所有温度和偏压下的微分电导和非平衡态密度。量子杂质系统的散射特性：提出了电子与磁性杂质的弹性和非弹性散射幅度的精确计算。精确的预测适用于所有温度和能量尺度，可用来描述：(I)在磁阻实验中测量的退相时间；(Ii)在大偏压下观察到的金属导线中的反常能量弛豫率。扩展的一维非平衡系统：提出一个概念框架来描述一些扩展的一维非平衡量子系统。

Non-Technical AbstractThis grant supports theoretical research involving the influence of impurities on the properties of systems such as quantum dots and nanoelectronics. In particular, the properties of these systems under nonequlibrium conditions will be studied. Most past work has been on equilibrium systems. However, nonequilibrium conditions are more realistic in actual applications. The project will involve the participation of graduate students and postdoctoral researchers.Technical AbstractIntellectual Merit: The study of non-equilibrium quantum impurity systems lies at theintersection of mesoscopic and strongly correlated physics. The dramatic recent advances in experimental techniques have allowed for the realization of impurity models in nanoscale devices such as quantum dots where quantum fluctuations are greatly enhanced due to low dimensionality. Describing the interplay between non-equilibrium conditions and strong correlations is a formidable intellectual challenge. This proposal addresses the issue of non-equilibrium steady states, a small corner of the more general problem . A new conceptual framework is proposed that allows for exact and explicit computations of the nonequilibrium steady state properties of quantum impurity models. In particular, it allows for the calculation of many experimentally measurable quantities such as the current across the dot and the nonequilibrium impurity density of states. The proposed framework also allows for the exact computation of scattering properties in quantum impurity models and consequently has strong implications for explaining such physical phenomena as decoherence and anomalous energy relaxation in metallic wires.Broader Impact: Non-equilibrium phenomena are ubiquitous in nature, and yet relativelypoorly understood. This stands in marked difference to equilibrium phenomena where a universal framework has been provided by Boltzmann more than a century ago. Steady states are the simplest among the great variety of non-equilibrium phenomena. This work will forge conceptual and practical tools to provide an exact description of steady-state dynamics in quantum impurity models. In the past, exact solutions have played an important role in increasing our understanding of equilibrium statistical mechanics. It is expected, therefore, that the proposed research will help point the way towards a general formulation of nonequilibrium steady-states by providing exact solutions for a set of models with important experimental realization. On a more practical level, the proposed research will help clarify the limits of applicability of nanodevices operating under temperature and voltage gradients. This has direct practical consequence for modern quantum electronics.The following projects will be studied:. Quantum impurities out of equilibrium: A new conceptual framework is proposedthat allows for the exact computation of the differential conductance and non-equilibriumdensity of states for a quantum dot described by the non-equilibrium Kondo or the Anderson models at all temperatures and bias voltages.. Scattering properties of quantum impurity systems: Exact computation of elastic and inelastic scattering amplitudes of an electron off a magnetic impurity is proposed.Precise predictions, valid for all temperatures and energy scales, will be available to describe: (i) the dephasing time as measured in experiments on magnetoresistance, and (ii) the anomalous energy relaxation rate observed in metallic wires under large bias voltage.. Extended 1D systems out of equilibrium: The development of a conceptual frameworkto describe some extended one-dimensional quantum systems out of equilibrium isproposed.