Deformation of a quantum many-particle system by a rotating impurity

TL;DR

This paper introduces a new canonical transformation that simplifies the complex angular momentum algebra in a many-particle quantum system with a rotating impurity, revealing an instability and deformation phenomena at a critical rotational speed.

Contribution

The authors develop a novel canonical transformation that makes the problem of a rotating impurity in a many-body bath exactly solvable in certain regimes, overcoming previous computational challenges.

Findings

Existence of a critical rotational speed causing angular momentum transfer.

Identification of a deformation in phonon density at the critical speed.

Exact solution of the impurity-bath system in the slow-rotation limit.

Abstract

During the last 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, their interactions with each other as well as with external fields. Due to 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 addition of an infinite number of angular momenta which renders it intractable using currently available techniques. Here, we introduce a novel canonical transformation which allows 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.