Disordered and Strongly Correlated Condensed Matter Systems

9400142费雪微观猝灭无序的存在往往会从本质上改变凝聚态系统的宏观行为。当无序控制热波动时，无序的影响在低温下表现得更加戏剧性。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如此强烈的量子系统，以至于用一个参考的非相互作用模型来简单描述是不合适的。这一理论研究将集中在这种强关联和无序系统的行为上。特别是，我们将研究以下问题：(1)分数量子霍尔效应中相互作用的一维电子气(Luttinger液体)和边态的输运；(2)无序分数和整数量子霍尔流体中平台之间的量子相变以及无序超导体中密切相关的超导体-绝缘体相变；(3)铜酸盐超导体混合态中的跨越到二维薄膜极限和非平衡涨落和噪声；(4)与小超导系统和与超导体接触的正常介观系统有关的介观超导电性。这项理论研究将集中在现代凝聚态物理学前沿的一些相关问题上。它们都有一个共同的主题，即物理无序和由所研究系统的量子性质引起的无序之间的竞争。虽然主要关注的是基本的凝聚态物理，但结果可能会对材料产生广泛的影响。要研究的系统包括新型高温超导体和二维电子气(如在强磁场中的半导体界面处发现的)。***

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). ***