Nonlinear Effects in Quantum Condensed Matter Systems

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TECHNICAL SUMMARYThis award supports theoretical research and education with an aim to develop nonperturbative methods for systems with strong interactions. The PI will focus on the hydrodynamic approach which provides a general framework for treating interacting systems. The PI aims to develop such an approach to gain insight into quantum low-dimensional strongly interacting systems focusing on integrable models. The linearized version of the hydrodynamic description, bosonization, is very effective in one-dimension. The PI plans to extend this approach to nonlinear and dispersive hydrodynamic theory. In contrast to linear bosonization, the nonlinear theory will be suitable for studying nonlinear effects, such as formation of dispersive shock waves. Shock waves have been observed in systems of cold atoms, and these new tools would be timely.The PI will study several physical systems such as cold atoms, quantum dots, two-dimensional electron gas in quantum Hall regime, and spin chains using topological methods and exact results for quantum mesoscopic transport.The PI is writing a review on the use of topological methods in quantum condensed matter physics and delivers tutorial lectures to researchers in condensed matter physics. The PI is developing a new course on topological aspects in solid state physics which will be taught to physics graduate students in Stony Brook. The PI teaches mathematics in K-12 enrichment program and teaches physics and mathematics to gifted high school students in Russia.NONTECHNICAL SUMMARYThis award supports theoretical research and education with the aim of developing a new approach for strongly interacting quantum mechanical systems, like electrons in strongly correlated materials and low temperature gases of atoms trapped by laser beams. The PI's approach builds on a method that has been successfully applied to systems confined to one dimension. The PI will use these methods to study some of the most challenging problems in condensed matter physics, such as spin chains and the nature of new states of matter predicted to exist in gases of electrons confined to dimensions in semiconductor crystals in a perpendicular strong magnetic field. These topological states of matter may enable a new kind of computation based on the manipulation of quantum mechanical states. Unlike other proposals for quantum computing, topological states would be comparatively immune from environmental effects that would interfere with the operation of a quantum computer.The PI is writing a review on the use of topological methods in quantum condensed matter physics and delivers tutorial lectures to researchers in condensed matter physics. The PI is developing a new course on topological aspects in solid state physics which will be taught to physics graduate students in Stony Brook. The PI teaches mathematics in K-12 enrichment program and teaches physics and mathematics to gifted high school students in Russia.