Correlated Electron Transport in Mesoscopic Structures

该奖项支持对量子低维和介观系统的动态响应和时间演化的理论研究。重点研究量子线、超导纳米电路和量子点实验的理论应用。动力来自于实验技术的进步，使动态响应测量成为可能，也来自于这些响应的评估对理论提出的挑战。本项目分为三个部分：1)PI将研究一维量子系统在高动量下的动态响应函数。这种状态对于量子线和自旋链的实验很重要，它要求发展非线性卢廷格液体理论。这项工作可能是朝着建立一维非线性量子流体的通用理论迈出的一步。本文将研究一种新的量子超导电路的动态机制——电感分流库珀对盒。这包括在小约瑟夫森结链中建立电荷波动的量子动力学理论。PI将解决与体导体接触的半导体量子点中的激子形成问题。光学吸收光谱中编码的近藤效应信息与直流输运实验中得到的信息是互补的。为了开展这项研究，PI将使用各种技术，包括图解扩展；费米液体理论；重整化群论；使用精确可解的一维模型；bosonization技巧;和数值方法。该研究为学生和博士后研究人员提供了教育经验。这个项目的工作发展了对真实材料的理解和对凝聚态理论的现代方法的熟练程度。该奖项支持理论研究和教育，以研究特殊种类的电线和其他结构的电子特性，这些结构能够将电子限制在一维甚至局部区域-有效的零维。就所含电子而言，普通导线是三维的。由于电子被限制在两个垂直方向上的距离越来越小，由此产生的电子流体的性质发生了巨大变化，导致了有趣的新现象。受最近实验进展的激励，PI将与实验接触，发展一种理论来理解这些低维电子流体的时间依赖特性。PI还将研究由超导体组成的电路，超导体在足够低的温度下表现出协同电子状态。超导是一种宏观状态，表现出相干性，这是原子和分子世界的量子力学状态的标志。PI将研究超导元素相互连接时出现的有趣的新现象。这项工作有助于量子计算的智力基础，在量子计算中，量子力学状态被操纵来执行逻辑运算。该项目促进了对新型系统和材料的理解，如纳米线、量子点和碳纳米管，这些都是未来电子技术的潜在元素。该项目致力于了解支撑这些系统的基本物理特性，因此可能会对技术产生影响。本研究为学生和博士后研究人员提供了教育经验。这个项目的工作发展了对真实材料的理解和对凝聚态理论的现代方法的熟练程度。

TECHNICAL SUMMARYThis award supports a theoretical investigation of the dynamic response and time evolution of quantum low-dimensional and mesoscopic systems. The research focuses on theory applicable to experiments with quantum wires, superconducting nano-circuits, and quantum dots. The motivation comes from the advances in experimental techniques enabling the dynamic response measurements and from the challenges the evaluation of these responses present for theory. The project has 3 parts:1.) The PI will investigate the dynamic response functions of one-dimensional quantum systems at high momenta. This regime, important for experiments with quantum wires and spin chains, calls for a development of the theory of a nonlinear Luttinger liquid. This work may be a step towards building a universal theory of one-dimensional nonlinear quantum fluids.2.) A new dynamic regime of a quantum superconducting circuit, an inductively shunted Cooper pair box, will be investigated. This includes building a theory of quantum dynamics of charge fluctuations in a chain of small Josephson junctions.3.) The PI will address exciton formation in a semiconductor quantum dot in contact with a bulk conductor. The information about Kondo effect encoded in the optical absorption spectra is complementary to that obtained in dc transport experiments.To carry out this research, the PI will use a variety of techniques, including diagrammatic expansions; Fermi liquid theory; renormalization group theory; the use of exactly solvable one-dimensional models; bosonization technique; and numerical methods.The research provides educational experiences for students and post-doctoral research associates. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory.NON-TECHNICAL SUMMARYThis award supports theoretical research and education to study the electronic properties of special kinds of wires and other structures which are able to confine electrons to one dimension or even to a localized region - effectively zero dimensions. Ordinary wires are three dimensional as far as the electrons they contain are concerned. As electrons are confined to ever smaller distances along two perpendicular directions, the properties of the resulting fluid of electrons change dramatically leading to interesting new phenomena. Motivated by recent experimental advances, the PI will be working in contact with experiment to develop a theory to understand the time dependent properties of these low-dimensional electronic fluids. The PI will also study circuits composed of superconductors which exhibit a cooperative electronic state at sufficiently low temperatures. Superconductivity is a macroscopic state that exhibits the property of coherence that is a hallmark of quantum mechanical states of the world of atoms and molecules. The PI will pursue interesting new phenomena that emerge when superconducting elements are interconnected. This work contributes to the intellectual foundations of quantum computing in which quantum mechanical states are manipulated to carry out logic operations.This project advances understanding of novel systems and materials, such as nano-wires, quantum dots, and carbon nanotubes, which are potential elements of future electronic technology. This project, devoted to understanding the fundamental physical properties that underpin these systems and as such may have a technological impact. This research provides educational experiences for students and post-doctoral research associates. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory.