Non-equilibrium dynamics of quantum many-body systems

Harvard University, Cambridge MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports fundamental theoretical research and education to advance conceptual understanding of quantum mechanical systems of many particles that are far from the balanced state of equilibrium, such as electrons in materials or large molecules in a strong electric field. As electronic devices shrink to ever smaller sizes, quantum mechanics becomes increasingly important to describe their operation which becomes further from equilibrium than current device technologies. Motivation for this research comes from experiments on nanostructures, assemblies of atoms that are on a scale some 100,000 times smaller than the diameter of a human hair, nanomechanical systems such as biomolecular motors, systems of atoms that are trapped by light and cooled near the absolute zero of temperature, and as well as optical systems. This award supports theoretical research to develop concepts that are universally applicable across diverse quantum systems such as these by exploiting the ability to carry out carefully controlled experiments in one area, for example systems of ultracold atoms to advance understanding in another, such as transport of electrons in nanostructures, in which owing to contact with the environment, it is difficult to achieve the same level of control in experiments. The research will be integrated with education at several levels from graduate level course development to pedagogical lectures at international summer and winter schools. TECHNICAL SUMMARY This award supports theoretical research and education to discover emergent universal behavior and to identify paradigms in the nonequilibrium dynamics of quantum many-body systems. The PI seeks to develop new concepts and new theoretical techniques motivated by experimental advances across condensed matter physics, ultracold atoms, and optics. The PI will use models, and theoretical and computational methods in close contact with experiments to study: relaxation and thermalization in nearly integrable systems, the conditions under which a hydrodynamic description is valid, the extent to which concepts from phase transitions and criticality apply, open and driven systems, and phenomena at the intersection of condensed matter and ultracold atom physics. The PI will develop new analytical and numerical methods aimed at understanding dynamical evolution of complex many-body systems. Analytical techniques will use exact Bethe ansatz solutions, perturbative expansions using nonequilibrium Keldysh formalism, the renormalization group approach, and analysis of effective field theories. Numerical approaches will include truncated Wigner approximation, time dependent dynamical mean-field renormalization group method, and dynamical mean-field theory calculations. The PI aims to exploit well controlled experiments on ultracold atoms together with theoretical advances to address the fundamental questions: Is there universality in nonequilibrium quantum dynamics at all? Is there emergent collective behavior which would enable the classification of quantum dynamics into several fundamental categories? The research will be integrated with education at several levels from graduate level course development to pedagogical lectures at international summer and winter schools.