Nonlinear and geometric effects in quantum condensed matter systems

点击翻译按钮获取中文摘要

Nontechnical SummaryThis award supports research and education in the development of theoretical methods to investigate strongly interacting quantum systems. Despite many recent advances, understanding these systems and developing appropriate theoretical tools remains one of the biggest challenges in condensed matter physics. Hydrodynamic methods are among few available approaches to the theory of strongly interacting systems. As the name implies, in certain situations it is feasible to view the complicated interacting quantum system as a fluid, and condense all the generally intractable details into virtual properties: density, velocity, viscosity, etc. As a result, phenomena well known from the study of fluids, such as vortices, shock waves, and turbulence, find analogs in systems of cold atoms or electrons. The project will lead the development of hydrodynamic approaches for a variety of condensed-matter and cold-atom systems. Part of the excitement associated with the proposed line of study stems from the opportunity to apply findings across different areas of research. The developed theoretical tools could be used in diverse fields of physics: quantum many-body theory, nonlinear dynamics, fluid dynamics, nuclear physics, cosmology, etc. The obtained results will be verified by numerical simulations and, ultimately, by comparison with experiments.The proposed research will provide a rich environment for the comprehensive training of graduate students in modern theoretical methods. The PI continues to give lectures on the uses of topology and geometry in condensed matter physics, and plans to prepare lecture notes for publication. The PI further plans to develop the notes into a book on topological aspects of condensed matter physics aimed at the broader community of scientists. The PI is enthusiastic about teaching math and physics to K-12 students in the enrichment program for children at Stony Brook, and to gifted high-school students in Russia.Technical SummaryThis award supports research and education in the development of theoretical methods to investigate strongly interacting quantum systems. Finding efficient ways to work with strongly interacting quantum systems is one of the most fundamental problems in condensed matter physics. It has been the focus of both experimental and theoretical research for the last three decades. To make progress in understanding systems with strong interactions, non-perturbative methods are needed. One of these few methods is the hydrodynamic approach, which provides a general framework for treating interacting quantum and classical systems. The project will develop new geometrical methods in condensed matter physics and look for applications to quantum transport phenomena.The proposed research is in the general direction of "geometrizing condensed matter physics", and progresses through the essential use of symmetries and effective descriptions. The PI expects to expand the understanding of the role of geometry in quantum many-body systems. The research uses geometric ideas and the hydrodynamic approach in studies of fractional quantum Hall systems and more general condensed matter systems. The proposed projects include thermal transport, and boundary-bulk relations for quantum Hall systems, anomalous hydrodynamics of quantum and classical systems, transport in chiral materials, and geometric aspects of out-of-equilibrium physics. Geometric ideas will be applied to analyze specific experiments on quantum transport.Part of the excitement associated with the proposed line of study stems from the opportunity to apply findings across different areas of research. The developed theoretical tools could be used in diverse fields of physics: quantum many-body theory, nonlinear dynamics, fluid dynamics, nuclear physics, cosmology, etc. The obtained results will be verified by numerical simulations and, ultimately, by comparison with experiments.The proposed research will provide a rich environment for the comprehensive training of graduate students in modern theoretical methods. The PI continues to give lectures on the uses of topology and geometry in condensed matter physics, and plans to prepare lecture notes for publication. The PI further plans to develop the notes into a book on topological aspects of condensed matter physics aimed at the broader community of scientists. The PI is enthusiastic about teaching math and physics to K-12 students in the enrichment program for children at Stony Brook, and to gifted high-school students in Russia.