Theoretical Problems in Condensed Matter and Statistical Physics

0233773 Halperin在此资助下进行的理论研究将提高我们对凝聚态和统计物理中各种现象的理解。 其中一些工作将试图解释现有实验中令人困惑的结果。 其他工作将旨在改进计算技术，了解现有理论模型的更广泛后果，或建议对理论思想进行新的实验测试。该项目将通过培训研究生、本科生和博士后研究员产生教育影响。 首席研究员还参与了向公众展示的工作，这可能会从这项研究中受益。大部分研究将涉及传导电子被限制在一个或多个方向的系统的特性。 作为这种系统的一个重要例子，场效应晶体管中的电子被捕获在半导体界面处，并且可以被描述为二维电子系统。 在低温强磁场中的二维电子系统中发现了许多令人惊讶的现象，统称为量子霍尔效应。 最近，实验已经在具有两个平行的二维电子系统的系统上进行，通过不同层中的电子之间的库仑相互作用耦合。 根据这项补助金的研究将开发各种状态的改进理论，这些状态可能发生在这样的系统中，包括弱耦合和强耦合相，以及电子密度可能在100 nm尺度上周期性变化的相。 拖动实验，其中一层中的电流在第二层中产生电压，在量子霍尔系统中显示出令人困惑的结果，本研究提出解释。 这项研究还将试图提高对测量电子穿过两层之间的势垒所产生的电导的实验的理解。 另一个研究领域将是一维电子系统的研究，它可以发生在碳纳米管中，也可以从半导体中的二维电子系统中制造出来。 以前的分析电子-电子相互作用对平行的一维线段之间的隧穿效应将扩展到更一般的实验参数范围。 其他的工作将尝试理解平行线的拖曳实验，并将探索半导体纳米线中的现象。另一个研究课题将探索近藤效应的普遍性，即局域电子的自旋的反复翻转在低温下的电输运中产生特殊的效应。 一般情况下，包括局部电子的位置变化，而不是它的自旋，引起异常传输效应的情况下，几个相互作用的电子的耦合运动是至关重要的。其他理论工作将探讨声波传播和含流体岩层中的NMR测量方面，这可能对油井管理有意义。在此资助下进行的理论研究将提高我们对凝聚态和统计物理学中各种现象的理解。 其中一些工作将试图解释现有实验中令人困惑的结果。 其他工作将旨在改进计算技术，了解现有理论模型的更广泛后果，或建议对理论思想进行新的实验测试。该项目将通过培训研究生、本科生和博士后研究员产生教育影响。 首席研究员还参与了向公众介绍情况的工作，公众可以从这项研究中受益。

0233773HalperinTheoretical research carried out under this grant will improve our understanding of a variety of phenomena in condensed matter and statistical physics. Some of the work will try to explain puzzling results from existing experiments. Other work will aim to improve calculational techniques, to understand the wider consequences of existing theoretical models, or to suggest new experimental tests of theoretical ideas.The project will have educational impact through the training of graduate students, undergraduates and postdoctoral fellows. The Principal Investigator is also involved in efforts to develop presentations to the general public, which could benefit from this research.A large portion of the research will concern properties of systems where conduction electrons are confined in one or more directions. As an important example of such a system, the electrons in a field-effect transistor are trapped at a semiconducting interface, and may be described as a two-dimensional electron system. A number of surprising phenomena, known collectively as quantum Hall effects, have been discovered in two-dimensional electron systems in strong magnetic fields at low temperatures. Recently, experiments have been carried out on systems with two parallel two-dimensional electron systems, coupled by the Coulomb interactions between electrons in different layers. Research under this grant will develop improved theories of the various states that can occur in such systems, including weakly and strongly coupled phases, and phases where the electron density may vary periodically in space on the scale of 100nm. Drag experiments, where current in one layer produces a voltage in the second layer, show puzzling results in quantum Hall systems, which this research proposes to explain. The research will also try to improve the understanding of experiments that measure the conductance arising from electrons that tunnel through the barrier between the two layers. Other work will try to understand shot noise measured in single-layer quantum Hall systems when current passes through a series of narrow constrictions.Another research area will be the study of one-dimensional electron systems, which can occur in carbon nanotubes, or can be fabricated out of two-dimensional electron systems in semiconductors. Previous analyses of the effects of electron-electron interactions on tunneling between parallel one-dimensional wire segments will be extended to more general ranges of experimental parameters. Other work will try to understand drag experiments with parallel wires, and will explore phenomena in semiconductor nanowires.Another research topic will explore generalizations of the Kondo effect, where repeated flips of the spin of a localized electron produce peculiar effects in electrical transport at low temperatures. Generalizations include situations where changes in the position of a localized electron, rather than its spin, give rise to anomalous transport effects: and situations where the coupled motion of several interacting electrons is crucial.Other theoretical work will explore aspects of sound propagation and of NMR measurements in fluid-containing rock formations, which could have significance for oil well management.%%% Theoretical research carried out under this grant will improve our understanding of a variety of phenomena in condensed matter and statistical physics. Some of the work will try to explain puzzling results from existing experiments. Other work will aim to improve calculational techniques, to understand the wider consequences of existing theoretical models, or to suggest new experimental tests of theoretical ideas.The project will have educational impact through the training of graduate students, undergraduates and postdoctoral fellows. The Principal Investigator is also involved in efforts to develop presentations to the general public, which could benefit from this research.***