Abstract
A group-theoretic treatment is given of the new phase found by Berry in the adiabatic evolution of a quantum-mechanical system in a finite-dimensional Hilbert space. It is shown how the Berry phases for the various eigenstates of the Hamiltonian are obtained from a set of angles associated with a group element. For the special case of a two-level system there is just one such angle which corresponds to the holonomy transformation associated with parallel transport around a closed curve on a sphere.
- Received 22 May 1986
DOI:https://doi.org/10.1103/PhysRevD.35.2597
©1987 American Physical Society