This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This award supports theoretical research and education focused on understanding fundamental aspects of quantum many-particle dynamics and their experimental consequences. A key goal is to develop a general formalism representing time evolution near various classical limits, for example particle, wave, mixed, rotational, etc., and apply it to various non-equilibrium systems. This work should significantly build on the PI's earlier work which proved the feasibility of this approach. The PI aims to pursue the possibility of analyzing the crossover from classical to quantum nonequilibrium behavior in various contexts. The PI intends to extend this formalism to fermionic systems and open systems coupled to a thermal bath. This representation of quantum dynamics will be contrasted with other existing approaches like the Keldysh technique and phase space methods. The PI's formalism together with other methods will be applied to specific problems of fundamental interest, including: thermalization in closed systems, dynamics of integrable and nonintegrable systems, formation of topological defects, perturbation of time evolution by external measurements, and slow and fast dynamics especially in low-dimensional systems. Special emphasis will be given to those applications, which can be tested in experiments. The research should lead to a better understanding of the role of the exponentially large Hilbert space on many-particle dynamics, how this exponential complexity becomes less and less relevant if one approaches the classical limit, and whether integrability of the system qualitatively affects various aspects of the quantum to classical crossover. The PI will also address other fundamental problems, including the conditions of existence and violation of adiabatic processes in closed systems. The PI will explore possibilities of using non-linear dynamical probes in closed systems to detect quasi-particle statistics, detect entanglement in low-dimensional systems, understand properties of asymptotic ensembles and connect them to statistics of work fluctuations and entropy generation. The role of nonintegrability, thermalization, and dimensionality of the system, which all likely play the crucial role in slow dynamics will be addressed. All major general theoretical results will be supplemented by specific proposals to experimentally test them in condensed matter, material, and cold atom systems.
The PI will be engaged in educational activities at the graduate level and higher to develop, refine, and enhance courses in quantum mechanics, statistical physics, many-body physics, and physics of cold atoms; contribute pedagogical review articles; and participate in international schools on advanced topics.
NON-TECHNICAL SUMMARY This award supports theoretical research and education focused on understanding the dynamics of quantum mechanical interacting many-particle systems. Examples of such systems include electrons in materials and specialized semiconductor structures and atoms cooled to very low temperatures and trapped by light. This research seeks to develop a theory for these kinds of system. Part of the research focuses on analyzing the dynamics of quantum systems using entirely the language of the trajectories given by classical mechanics. This work highlights nontrivial connections between quantum dynamics, classical dynamics, and statistical physics. The PI also aims to advance understanding of driven quantum mechanical interacting many-body systems.
The understanding of the dynamics of quantum mechanical many-body systems has broad consequences and contributes to intellectual foundations that may lead to future technologies.
The PI plans to develop educational materials intended for a broad audience of non-specialists and to actively participate in domestic and international conferences, workshops, and schools.
