Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

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NONTECHNICAL SUMMARYThis award supports theoretical research on complex quantum systems that are in a highly excited or nonequilibrium state. These systems can be realized in a myriad of experimental platforms, and they are also ingredients in the next generation of devices. Theoretical methods to study such systems are, however, still in their infancy. Quantum systems also have a defining feature, called quantum entanglement, that makes them qualitatively different from their classical counterparts. This project will develop theoretical methods to study not only classical metrics of quantum systems such as resistance and viscosity, but will also develop techniques to study quantum entanglement. The study of entanglement is well aligned with the NSF Quantum Leap initiative, whose goal is to push the boundaries of quantum mechanics and its applications to next generation technologies.This project also has a strong educational component as it will lead to the training of the next generation of scientists. The PI and NSF funded research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. The PI is also committed to organizing a series of conferences that aim to bring together diverse communities of scientists that usually do not have the opportunity to interact, but share the common goal of understanding nonequilibrium phenomena in complex systems. TEHCNICAL SUMMARYThis award supports theoretical research on nonequilibrium phenomena in strongly correlated quantum systems. The project will develop field-theoretic approaches to study transport, correlation functions, and entanglement measures far out of equilibrium. The development of a formalism for studying entanglement measures is well aligned with the NSF Quantum Leaps initiative. The project also applies to current experiments in cold-atomic gases, ultra-fast pump-probe spectroscopy of solid-state systems, and light-matter coupled systems. The project has the following major components: (1) Large-N bosonic and fermionic theories, along with the two-particle irreducible formalism that naturally takes into account conservation laws, will be employed to study nonequilibrium phenomena. Transient conductivity and viscosity following a quantum quench will be studied. Interacting critical systems will be studied, with the goal of searching for new scaling physics out of equilibrium and exploring whether critical slow modes can give rise to anomalies in transport. (2) An augmented Schwinger-Keldysh formalism will be employed to study out of time ordered correlators, and the Renyi entanglement entropy. Controlled weak-coupling expansions will be developed to construct these entanglement measures. The project also has a strong educational component as it will lead to the training of a graduate student and a postdoctoral research scientist. The PI and NSF funded research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. The PI is also committed to organizing a series of conferences that aim to bring together diverse communities of scientists who share the common goal of understanding nonequilibrium phenomena in complex systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.