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.
Intellectual Merit: Recent advances in nanotechnology are resulting in the rapid miniaturization of devices. At the same time advances in micro-optics are allowing for the creation of novel systems where light and matter interact strongly. One distinguishing feature of these new class of systems is the achievement of highly tunable interacting quantum systems that are also far out of equilibrium with their environment, a situation in which general laws of thermodynamics no longer hold, and concepts such as temperature are no longer valid. Theoretically understanding the properties of such systems is hugely challenging. One of the goals of this project was to develop theoretical methods to help conceptually understand what kind of collective quantum states of matter can be realized under out of equilibrium conditions. The project involved the theoretical study of two kinds of systems. One were systems realizable in nanotechnology and correspond to current carrying wires that are coupled to tiny magnetic elements that fluctuate strongly due to quantum effects. General results were obtained for how the resistance of the system behaves. It was shown that current flow can induce a change in the phase of the system where the magnetic moments gradually stop being aligned with each other as the magnitude of the current is increased. The second system that was studied are thermally isolated quantum gases that can be manipulated using micro-optics. Here the project explored how these isolated quantum systems evolve in time after being prepared in a certain way. A phenomenon known as thermalization was explored where systems eventually lose memory of their initial state, with their behavior again described by the laws of thermodynamics. What are the precise conditions for thermalization, and how long does the system take to thermalize are some of the fundamental open questions that were explored. We showed that for closed quantum systems undergoing unitary dynamics, it is only a reduced part of the system that thermalizes by being characterized by an effective temperature which makes this reduced sub-system appear classical. The remaining part of the system acts as an effective reservoir by being a source of dissipation and noise for the reduced part. On the other hand the system as a whole continues to be in a pure quantum state with no simple description in terms of a temperature. Nonequilibrium many-particle systems are hard to study, yet we could make progress by showing that even out of equilibrium, separation of time and length scales may exist that allows one to use a coarse-graining procedure to study their properties. Broader Impacts: The project has involved the active participation and training of two doctoral students who have written several papers in peer reviewed journals and have presented their results at leading conferences. One of these students obtained his PhD in 2012 and went on to take up a physics teaching position at a liberal arts college. The second graduate student will obtain his PhD in 2015 and is expected to take up a postdoctoral research position. In addition each summer an NYU undergraduate student has worked on the projects under the supervision of the PI and the graduate students. Thus the NSF funding has been critical for training young scientists, preparing them to take up leadership positions either in a research or in a teaching program. The project has also resulted in the development of new techniques for studying out of equilibrium quantum systems. The methods developed have a broad applicability across several disciplines in science such as quantum information, device engineering and quantum chemistry.
