Interacting, Disordered, Electrons: Two Tractable Limits

相互作用、无序电子：两个可处理的极限

• 批准号: 0311761
• 负责人: Ganpathy Murthy
• 金额: $ 30万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311761&HistoricalAwards=false
• 关键词: Interacting; Disordered; Electrons; Two; Tractable

The focus of this theoretical research is to investigate the interplay of interactions and disorder in two tractable limits, with clear implications for the more generic problem. The first tractable case is the mesocopic one. Here there are two energy scales, the single-particle level spacing and the Thouless energy, which is connected by the uncertainty principle to the time for an electron to sample the system. The ratio of these two is the dimensionless conductance, g. In the limit of large g, the problem of disorder and (Fermi-liquid) interactions is completely solvable in the same sense as a conventional large-N theory. This approach is nonperturbative in both disorder and interactions, thanks to the small parameter 1/g. Interesting phase transitions and slow collective modes also emerge in this new framework, which allows one to understand experimental and numerical results on large Coulomb blockade fluctuations in quantum dots, and potentially the sign and magnitude of persistent currents in mesoscopic rings.The second tractable limit is in the integer/fractional quantum Hall elects, where strong interaction results in gaps which enable a controlled incorporation of the effects of disorder. A new Hamiltonian approach to the fractional quantum Hall regime makes it possible to calculate physical quantities using very simple approximations (because the nonperturbative properties of the quasiparticles, such as their fractional charge, have been incorporated into the theory). This formalism will be used to treat the gapped fractional quantum Hall states and the very interesting Fermi liquid state in the half-filled Landau level in the presence of disorder.The project will have a broad impact in training of a postdoctoral research associate; in stimulating experimental activity to verify the predictions of the theory; and it may have implications for the use of quantum dots in quantum computation.%%% The focus of this theoretical research is to investigate the interplay of interactions and disorder in two tractable limits, with clear implications for the more generic problem. The first tractable case is the mesocopic one, which includes quantum dots. The second case is in the quantum Hall regime.The project will have a broad impact in training of a postdoctoral research associate; in stimulating experimental activity to verify the predictions of the theory; and it may have implications for the use of quantum dots in quantum computation.***

这项理论研究的重点是研究两个可拖动限制的相互作用和混乱的相互作用，对更通用的问题产生了明显的影响。 第一个可拖动的情况是中焦。 这里有两个能量尺度，即单粒子水平的间距和无能的能量，这些能量是由不确定性原理连接到电子对系统采样的时间的。 这两个的比例是无量纲电导，g。 在大G的极限中，与常规的大N理论相同的意义上，混乱和（费米 - 液体）相互作用的问题是完全可解决的。 得益于小参数1/g，这种方法在疾病和相互作用中都是不受欢迎的。 在这个新框架中，有趣的相变和缓慢的集体模式也会出现，该框架可以理解量子点中大型库仑阻塞的波动的实验和数值结果，以及潜在的介质环中持久电流的符号和幅度。第二次拖延极限是在完整的/分数量子霍尔的互动中的第二次拖动，在这种情况下构成了互动的效果，这些效果的互动成果构成了与互动的相互作用。 一种新的哈密顿量方法对分数量子厅制度的方法可以使用非常简单的近似值来计算物理量（因为准粒子的非扰动特性（例如其分数电荷）已被纳入理论中）。 这种形式主义将用于治疗分数量子厅状态，在疾病存在下，在半充满的兰道水平上的非常有趣的费米液态。刺激实验活性以验证理论的预测；这可能对在量子计算中使用量子点有影响。%% %%这项理论研究的重点是研究两个可行限制的相互作用和混乱的相互作用，对更通用的问题有明显的影响。 第一个可拖动的情况是中载含量，其中包括量子点。 第二种情况是在Quantum Hall制度中。该项目将对博士后研究助理培训产生广泛的影响。刺激实验活性以验证理论的预测；它可能对在量子计算中使用量子点有影响。***