1202.2908 (B. Zygelman)

Geometric gauge potentials and forces in low-dimensional scattering
systems    [PDF]

B. Zygelman

We introduce and analyze several low-dimensional scattering systems that
exhibit geometric phase phenomena. The systems are fully solvable and we
compare exact solutions of them with those obtained in a Born-Oppenheimer
projection approximation. We illustrate how geometric magnetism manifests in
them, and explore the relationship between solutions obtained in the diabatic
and adiabatic pictures. We provide an example, involving a neutral atom dressed
by an external field, in which the system mimics the behavior of a charged
particle that interacts with, and is scattered by, a ferromagnetic material. We
also introduce a similar system that exhibits Aharonov-Bohm scattering. We
propose some practical applications. We provide a theoretical approach that
underscores universality in the appearance of geometric gauge forces. We do not
insist on degeneracies in the adiabatic Hamiltonian, and we posit that the
emergence of geometric gauge forces is a consequence of symmetry breaking in
the latter.

View original: http://arxiv.org/abs/1202.2908