Schmidt, Richard ; Lemeshko, MikhailIST Austria
During the past 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, and their interactions with each other as well as with external fields. Because of the properties of quantum rotations, the angular-momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems. In this work, we study an example of the latter: A rotating quantum impurity coupled to a many-body bosonic bath. In the regime of strong impurity-bath couplings, the problem involves the addition of an infinite number of angular momenta, which renders it intractable using currently available techniques. Here, we introduce a novel canonical transformation that allows us to eliminate the complex angular-momentum algebra from such a class of many-body problems. In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly rotating impurity. We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath. Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.
Physical Review X
We are grateful to Eugene Demler, Jan Kaczmarczyk, Laleh Safari, and Hendrik Weimer for insightful discussions. The work was supported by the NSF through a grant for the Institute for Theoretical Atomic, Molecular, and Optical Physics at Harvard University and Smithsonian Astrophysical Observatory.
Schmidt R, Lemeshko M. Deformation of a quantum many-particle system by a rotating impurity. Physical Review X. 2016;6(1). doi:10.1103/PhysRevX.6.011012
Schmidt, R., & Lemeshko, M. (2016). Deformation of a quantum many-particle system by a rotating impurity. Physical Review X, 6(1). https://doi.org/10.1103/PhysRevX.6.011012
Schmidt, Richard, and Mikhail Lemeshko. “Deformation of a Quantum Many-Particle System by a Rotating Impurity.” Physical Review X 6, no. 1 (2016). https://doi.org/10.1103/PhysRevX.6.011012.
R. Schmidt and M. Lemeshko, “Deformation of a quantum many-particle system by a rotating impurity,” Physical Review X, vol. 6, no. 1, 2016.
Schmidt R, Lemeshko M. 2016. Deformation of a quantum many-particle system by a rotating impurity. Physical Review X. 6(1).
Schmidt, Richard, and Mikhail Lemeshko. “Deformation of a Quantum Many-Particle System by a Rotating Impurity.” Physical Review X, vol. 6, no. 1, 011012, American Physical Society, 2016, doi:10.1103/PhysRevX.6.011012.