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RUI: NSF/DMR-BSF: Nonequilibrium Quantum Matter: Timescales and Self-Averaging: Yeshiva University

Lea Ferreira dos Santos

[email protected]

NONTECHNICAL SUMMARY<br/>This award supports a theoretical and computational research collaboration between a PI funded by the National Science Foundation and a PI funded by the Israel Binational Science Foundation (BSF). The collaboration will combine complementary skills and resources to perform computational and theoretical studies of systems comprised of many interacting particles that are far from the state of equilibrium and which are described by quantum mechanics. The properties of systems in equilibrium do not change in time. In contrast the properties of nonequilibrium systems like, for example, the electrons in a nanomaterial that has been exposed to a burst of light, change. This research aims to advance understanding of how systems far from equilibrium relax to achieve the equilibrium state. The PI's aim is to further understand the dynamical behavior of quantum mechanical systems driven by external fields. <br/><br/>Understanding the properties of many-body quantum systems out of equilibrium is a fundamental problem of great interest to many fields, including atomic, molecular, and condensed matter physics, quantum information science, and cosmology. The team's studies may lead to:<br/>*) the prediction and discovery of new phases of matter that only appear in quantum systems out of equilibrium. New phases of matter are tightly connected with the development of new materials needed in emerging technologies and to improve existing device technologies. <br/>*) insight into quantum computing. The models used in these studies are analogous to those used in the development of technologies that manipulate quantum mechanical states to perform computation, quantum computing. Advances in the understanding of many-body quantum systems can lead to revolutionary developments in both computational capabilities and encryption technologies.<br/><br/>This project will foster the participation of women in STEM fields by engaging female undergraduate students in the research. It will help motivate young women to study physics by giving presentations about what can be done with a degree in physics in venues like open houses and visits to high schools for girls. The PI also aims to modernize the curriculum at Stern College for Women by integrating computational activities into the undergraduate science courses. Computer codes and tutorials developed through this project will be posted online to contribute to the integration of teaching and research at other institutions. The collaboration will also benefit the undergraduate students of Stern College for Women, who will have the opportunity to experience research at a PhD granting institution in Israel.<br/><br/><br/>TECHNICAL SUMMARY<br/>This award supports a theoretical and computational research collaboration between a PI funded by the National Science Foundation and a PI funded by the Israel Binational Science Foundation (BSF). The collaboration will combine complementary skills and resources with an aim to advance understanding of the dynamics of many-body quantum systems, an outstanding challenge at the forefront of theoretical and experimental physics. It bridges fields as diverse as atomic, molecular, condensed matter, and high-energy physics. The widespread interest in the subject is prompted by new theoretical and computational methods, and by experimental access to ever longer coherent evolutions. Particular attention has been given to the conditions for equilibration, thermalization, and localization in interacting systems described by static and driven Hamiltonians, themes to which both the PI and the BSF-PI have made several important contributions. Yet, a challenging question that remains open refers to the time for these systems to equilibrate. Existing results, often based on abstract models, are contradictory. Also debated are: the time that marks the onset of universal behavior, what Thouless time is in interacting systems, the duration of exponential behaviors, and how these timescales relate with the heating timescale of driven systems. To characterize these various timescales, the team will consider realistic models and experimental observables, and will take advantage of their experience with quantum chaos and random matrix theory to identify general behaviors and derive analytical expressions. While the PI has mostly focused on time-independent Hamiltonians, the BSF-PI will bring in his expertise on driven systems. In addition to dynamics and timescales, self-averaging will also be a central topic of this project. Contrary to ergodicity, self-averaging in interacting quantum systems out of equilibrium has received very little attention, despite its importance to the development of theoretical models, as well as to experiments and numerical simulations, where access to many realizations may be costly.<br/><br/>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.

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