Nonequilibrium Quantum Mechanics of Strongly Correlated Systems

New York University, New York NY

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education to advance fundamental understanding of the properties of strongly correlated quantum systems that have been driven far from equilibrium. This research is motivated by experiments on nonequilibrium quantum systems. Using Keldysh diagrammatic methods, the PI has shown how powerful concepts such as mean-field theory, identifying the important fluctuations about mean-field and the renormalization group can be generalized to a variety of nonequilibrium problems. The PI will further build on these ideas and apply them to the following systems: a). Nonequilibrium quantum impurity models which show rich behavior in equilibrium such as non-Fermi liquid physics and quantum phase transitions. b). Spatially extended systems near dissipative quantum critical points and driven out of equilibrium by current flow. c). Strongly correlated systems subjected to strong time dependent perturbations such as a sudden change of a parameter of the Hamiltonian, or by photo-excitation by strong transient light pulses. These projects will be relevant to a number of experimental systems such as: nonequilibrium nanoscale devices, cold atoms in optical lattices with rapidly tunable parameters, nonlinear optical spectroscopies of strongly correlated systems and transport near quantum critical points. Fundamental questions that will be addressed include: a). Systems near equilibrium quantum critical points show universal behavior. Do notions of universality still hold when these systems are driven out of equilibrium? b). To what extent is an "effective temperature" description of nonequilibrium systems valid? c). Can a nonequilibrium drive such as uniform current flow give rise to new kinds of time-independent or time-dependent dynamical phases? d). Is it possible to realize nonequilibrium driven ``ordering-disordering'' quantum phase transitions? If so can such transitions be characterized by universality and critical exponents? This award also supports guidance and training of graduate and undergraduate students in an emerging area of science. NON-TECHNICAL SUMMARY: This award supports theoretical research and education aimed towards understanding many particle systems that require a quantum mechanical description and are out of balance with their surroundings because of a large perturbation. Applying a voltage to electrons in a material with very small dimensions the size of molecules, otherwise known as a nanostructure, would be an example. For these systems, the successful theoretical methods developed to understand and describe systems that are in balance with their surroundings do not work and the PI aims to develop extensions of these equilibrium methods to nonequilibrium systems. This general problem also arises in atomic and optical physics, biological systems, and quantum information theory and the PI's approach should apply to a broad range of nonequilibrium systems. The PI will build on her previous work and study nanostructures out of equilibrium and explore the possibility that an electric current can drive materials that are near a transformation to magnetism or superconductivity into new states of matter that may not exist in equilibrium. She will also study nonequilibrium quantum systems that have many strongly interacting particles, such as strongly correlated materials subjected to intense transient pulses of light. This research contributes to the broad fundamental understanding of the world around us. The focus of the research on nanostructures and systems of impurities contributes to the theoretical foundations that will enable the design of possible future electronic devices and information technology. This award also supports guidance and training of graduate and undergraduate students in an emerging area of science.