Technological progress has enabled scientists and engineers to build and manipulate physical systems at the level of individual atoms and molecules. At these small scales the laws of Nature are often strange and counter-intuitive. This award supports theoretical research and education aimed to elucidate how the dynamics of such systems can be controlled, and to deepen understanding of how the laws of quantum physics and thermodynamics combine to determine the behavior of nanoscale systems.
Quantum physics governs the behavior of atoms and molecules, while thermodynamics was developed to describe how systems exchange energy and matter with one another. Combining the two fields, particularly for systems that are far away from the steady state of thermal equilibrium is a challenging area of research. The activities funded by this award will address three aspects of this problem. One project involves developing theoretical methods for controlling a quantum mechanical system so that it reaches a desired final state in a fixed amount of time. This will involve theoretical tools borrowed from quantum physics, classical mechanics and thermodynamics. The second project is aimed to explore how thermodynamic concepts such as heat and work apply to systems that are governed by the laws of quantum physics. In the third project, the PI will investigate the role played by the interactions between a small system and its surroundings, in the thermodynamic behavior of the system.
These activities will involve students as well as postdoctoral researchers, providing training in theoretical methods at the intersection of quantum physics and thermodynamics.
This award supports fundamental theoretical research and education related to the coherent quantum control and the thermodynamics of systems at atomic and molecular length scales. The first project addresses the new and exciting field of shortcuts to adiabaticity, where the aim is to guide a system to evolve as if it were being manipulated very slowly, even when the manipulation occurs rapidly. The PI will develop strategies that apply the tools of classical and statistical physics to design such quantum shortcuts. The second project undertakes a careful analysis of the relationship between classical and quantal definitions of work, with an emphasis on using semiclassical methods to identify the impact of quantum interference between classical trajectories. The third project involves investigating how the first and second laws of thermodynamics "scale down" to describe the behavior of systems that are strongly coupled to their thermal surroundings. The PI will explore microscopically precise definitions of quantities such as internal energy, entropy and volume that preserve the structure of the first and second laws, without needing to introduce corrections to account for strong system-environment interaction.
The proposed research will:
(1) Develop a broadly applicable methodology for using classical mechanics to design protocols for the manipulation of coherent quantum systems. This methodology will be useful in experimental settings where many of the current methods, based on scale-invariant driving, do not apply. (2) Provide a deeper understanding of the emergence of classical thermodynamics from quantum thermodynamics, for isolated systems driven by the variation of external parameters. In particular, it will clarify the role of quantum interference on the second law of thermodynamics and on nonequilibrium fluctuation relations. (3) Establish a consistent, microscopic thermodynamic framework for describing the interchange of energy between a system and its surroundings, when the two are sufficiently strongly coupled that the interaction energy itself cannot be ignored. This framework will be useful in describing the thermodynamics of biomolecules, which interact strongly with their aqueous surroundings.
This award supports graduate student and postdoctoral level training in the methods of theoretical and computational statistical physics.
