Disordered and Strongly Correlated Condensed Matter Systems

[400142 Fisher]微观猝灭无序的存在常常从质的上改变凝聚态体系的宏观行为。在低温下，无序的影响比热波动更明显。然而，在低温下，通常有必要解开无序和量子涨落之间微妙的相互作用。特别具有挑战性的是那些相互作用非常强的量子系统，用参考非相互作用模型的简单描述是不合适的。这一理论研究将集中在这种强相关和无序系统的行为上。主要研究以下问题：(1)一维电子气体（Luttinger液体）相互作用中的输运和分数量子霍尔效应中的边缘态；(2)无序分数和整数量子霍尔流体中平台间的量子相变以及与之密切相关的无序超导体-绝缘体相变；(3)铜超导体混合态的二维薄膜极限交叉和非平衡波动和噪声；(4)与小型超导系统和与超导体接触的普通介观系统相关的介观超导性。本理论研究将集中于现代凝聚态物理前沿的若干相关问题。它们都有一个共同的主题，即被研究系统的量子性质引起的物理混乱和混乱之间的竞争。虽然主要关注的是基本的凝聚态物理，但结果可能对材料产生广泛的影响。研究的系统包括新型高温超导体和二维电子气体（在强磁场中发现的半导体界面）。＊＊＊

9400142 Fisher The presence of microscopic quenched disorder often changes qualitatively the macroscopic behavior of condensed matter systems. The effects of disorder are revealed even more dramatically at low temperatures when they dominate over thermal fluctuations. At low temperatures, though, it is often necessary to disentangle the subtle interplay between disorder and quantum fluctuations. Particularly challenging are those quantum systems in which the interactions are so strong that a simple description in terms of a reference non-interacting model are inappropriate. This theoretical research will focus on the behavior of such strongly correlated and disordered systems. In particular, the following problems will be studied: (1) Transport in interacting one- dimensional electron gases (Luttinger liquids) and edge states in the fractional quantum Hall effect; (2) The quantum phase transition between plateaus in disordered fractional and integer quantum Hall fluids and the closely related superconductor- insulator transition in disordered superconductors; (3) The crossovers to the two-dimensional thin film limit and non- equilibrium fluctuations and noise in the mixed state of the cuprate superconductors; (4) The mesoscopic superconductivity associated with small superconducting systems and with normal mesoscopic systems in contact with superconductors. %%% This theoretical research will focus on a number of related problems at the forefront of modern condensed matter physics. They all have the common theme of competition between physical disorder and disorder induced by the quantum nature of the systems being studied. While the primary focus is on fundamental condensed matter physics, the results have potential for a broad impact on materials. The systems to be studied include the new high temperature superconductors and the the two-dimensional electron gas (as found at semiconductor interfaces in strong magnetic fields). ***