Defects and Fluctuations in Low-Dimensional Condensed Matter

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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.***