Dynamics and Thermodynamics of Nanoscale Systems

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on foundations of the control and application of quantum mechanical systems. The first theme of this project involves the ability to control microscopic systems that obey the counter-intuitive laws of quantum physics. Technological progress has brought us to the point where experimentalists can isolate, observe, and manipulate individual quantum systems. The PI and his group will develop new strategies for controlling how quantum systems evolve with time. One approach will use impulses, in which the system is briefly subjected to very strong external forcing, causing its state to change quickly. This project will develop the theory needed to design impulses to achieve a desired change in the system’s state. Another approach will involve Thouless pumping, a quantum-mechanical analogue of Archimedes’ screw that can be used to transport electrons. The original theoretical proposal by Thouless in 1983, which has been verified experimentally during the past decade, requires that the pumping be carried out very slowly. The PI and his group will apply new techniques from the field of Shortcuts to Adiabaticity, to accelerate the transport of electrons by Thouless pumping. The second theme of this project addresses systems that are driven by an external force that oscillates periodically with time, causing the system to absorb energy. When these oscillations are very fast, it has been found that energy absorption is greatly suppressed. This project will explore whether this behavior can be understood in terms of a simple picture in which the system’s energy performs a “biased random walk”. The PI and his group will investigate this question both for systems that obey familiar laws of classical physics and for those that obey the laws of quantum mechanics. If the biased random walk hypothesis proves to be accurate, it will provide a quantitative theory for predicting the rate energy is absorbed by rapidly and periodically driven systems, which will be useful in proposed applications of such out-of-equilibrium systems. The educational component of this project will involve the training of students in a strongly collaborative, supportive and cross-disciplinary environment. Research results will be disseminated through publications in scientific journals as well as presentations at conferences and other venues. The PI will regularly give colloquium-level presentations aimed at introducing a broad scientific audience to recent progress in non-equilibrium statistical physics, and will write a graduate-level textbook on this field based on a course he has developed and taught multiple times at the University of Maryland. TECHNICAL SUMMARY This award supports theoretical research and education to investigate strategies for controlling the dynamics of quantum systems, with a particular focus on accelerated evolution. Impulses are familiar from undergraduate-level classical physics but have received less attention in quantum physics. This project will specifically address “super”-impulses, in which the strength of the impulses scales inversely with the square of its duration. Preliminary results reveal that such super-impulses cause a wavefunction to change in a non-trivial manner that can be described entirely in terms of classical trajectories, without invoking the semiclassical limit. The project will also address the phenomenon of Thouless pumping, in which electrons are transported via a topological effect. While in its original version Thouless pumping is adiabatic (quasi-static), the PI and his research team will explore non-adiabatic extensions of Thouless pumping, making use of recently developed tools from the field of Shortcuts to Adiabaticity. The project will also investigate the phenomenon of prethermalization, which refers to the exponential suppression of energy absorption by systems driven rapidly and periodically with time. In preliminary results, the PI and his group have proposed a Fokker-Planck equation describing energy absorption in this scenario. The research activity will include validating this equation in a number of model systems, exploring whether it quantitatively describes prethermalization, and extending these results to quantum systems through a model that combines Fermi’s Golden Rule with a semiclassical treatment of quantum energy transitions.The educational component of this project will involve the training of students in a strongly collaborative, supportive and cross-disciplinary environment. Research results will be disseminated through publications in scientific journals as well as presentations at conferences and other venues. The PI will regularly give colloquium-level presentations aimed at introducing a broad scientific audience to recent progress in non-equilibrium statistical physics, and will write a graduate-level textbook on this field based on a course he has developed and taught multiple times at the University of Maryland.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.