Year: 2023
Type: preprint
Abstract: We use the Van Vleck-Primas perturbation theory to study the problem of parallel transport of the eigenvectors of a parameter-dependent Hamiltonian. The perturbative approach allows us to define a non-Abelian connection $\mathcal{A}$ that generates parallel translation via unitary transformation of the eigenvectors. It is shown that the connection obtained via the perturbative approach is an average of the Maurer-Cartan 1-form of the one-parameter subgroup generated by the Hamiltonian. We use the Yang-Mills curvature and the non-Abelian Stokes' theorem to show that the holonomy of the connection $\mathcal{A}$ is related to the Berry phase.
Source: arXiv (Cornell University)
Authors: Manjarres, A. D. Bermúdez, Botero, A.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367860099