Defects and Fluctuations in Low-Dimensional Condensed Matter

该奖项涉及凝聚态物理的理论研究，以研究低维缺陷和涨落。拓扑缺陷在我们理解凝聚态物质中的许多物理现象中起着核心作用，特别是在低维系统中，由于热或量子涨落，自发有序往往是不可能的。这些系统的状态通常以缺陷为特征，这些缺陷可能会扩散也可能不会扩散。这项研究建议对各种低维系统进行研究，在这些系统中，缺陷和/或涨落扮演着重要的角色，对于二维缺陷解除结合的范例--Kosterlitz-Thouless转变--不适用的情况。这些研究将探索一种新的转变机制的性质和结果，当存在对称破缺场时，这种机制在低有效温度下导致缺陷的线性限制，而在较高温度下通过弦扩散机制来解除限制。研究的系统将包括光学晶格中的玻色子、一维量子系统、双层量子霍尔系统和超导薄膜。此外，研究还将集中在量子霍尔系统中的异常物理。其中最突出的是对双层膜中层间相干的研究，最近显示出类似超导电性的性质。我们还将研究量子霍尔液晶态，特别是条纹和气泡。这项工作的更广泛影响将是为理解低维系统开发新的方法，这些方法可能对广泛的凝聚态和材料系统有用。此外，这项工作将与学生和博士后一起完成，涉及分析方法和数值模拟，这将是他们专业培训的一部分。结果将通过出版物、研讨会和会议报告向物理界报告，并在可能的情况下，通过通俗水平的文章、学术讨论会和公开报告向更广泛的社区报告。%该奖项涉及凝聚态物理的理论研究，以研究低维缺陷和涨落。在比我们正常的三维世界更小的维度上，物质的物理学往往是不同的。例如，在固体表面上运动的电子与在固体内部运动的电子的行为不同。这项研究研究了与这些系统中的缺陷有关的低维发生的新现象。这些缺陷通常与凝聚系统的正常周期几何结构的变化有关。这项工作的更广泛的影响将是开发新的方法来理解低维系统，这些方法可能在广泛的凝聚态物质和材料系统中有用。此外，这项工作将与学生和博士后一起完成，涉及分析方法和数值模拟，这将是他们专业培训的一部分。结果将通过出版物、研讨会和会议报告向物理界报告，并在可能的情况下通过通俗水平的文章、座谈和公开报告向更广泛的社区报告。

This award involves theoretical research in condensed matter physics to study defects and fluctuations in low dimensions. Topological defects play a central role in our understanding of many physical phenomena in condensed matter, particularly low-dimensional systems where spontaneous order is often not possible due to thermal or quantum fluctuations. The state of these systems is often characterized by defects which may or may not proliferate. This research suggests studies of a variety of low -dimensional systems in which defects and/or fluctuations play an important role, for situations where the paradigm of defect unbinding in two dimensions - the Kosterlitz-Thouless transition - does not apply. The studies will explore the properties and consequences of a novel transition mechanism operative when a symmetry-breaking field is present, leading at low effective temperature to linear confinement of defects, and deconfinement via a string-proliferation mechanism at higher temperature. The systems studied will include bosons in optical lattices, one-dimensional quantum systems, bilayer quantum Hall systems, and thin superconducting films.In addition to this, the research will focus on unusual physics in quantum Hall systems. Prominent among these will be studies of interlayer coherence in bilayers, which recently have shown properties akin to superconductivity. Quantum Hall liquid crystal states, especially stripes and bubbles, will also be examined.The broader impact of this work will be to develop new methods for the understanding of low-dimensional systems that may be useful in a broad array of condensed matter and materials systems. In addition, the work will be done in conjunction with students and postdocs, and involves both analytical methods and numerical simulations that will be part of their professional training. The results will be reported to the physics community through publications, seminars, and conference presentations, and, when possible, to the broader community through popular-level articles, colloquia, and public presentations.%%% This award involves theoretical research in condensed matter physics to study defects and fluctuations in low dimensions. The physics of matter in dimensions less than our normal three-dimensional world is often different. For instance, electrons moving on surfaces of solids behave differently than electrons moving in the interior of the solid. This research studies novel phenomena occurring on low-dimension having to do with defects in these systems. These defects are usually associated with a change in the normal, periodic geometry of the condensed system.The broader impact of this work will be to develop new methods for the understanding of low-dimensional systems that may be useful in a broad array of condensed matter and materials systems. In addition, the work will be done in conjunction with students and postdocs, and involves both analytical methods and numerical simulations that will be part of their professional training. The results will be reported to the physics community through publications, seminars, and conference presentations, and, when possible, to the broader community through popular-level articles, colloquia, and public presentations.***