Geometric gauge potentials and forces in low-dimensional scattering systems

摘要

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena.nThe systems are fully solvable and we compare accurate solutions of them with those obtained in a Born-nOppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explorenthe relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example,ninvolving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particlenthat interacts with, and is scattered by, a ferromagnetic material.We also introduce a similar system that exhibitsnAharonov-Bohm scattering. We propose possible practical applications. We provide a theoretical approach thatnunderscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in thenadiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetrynbreaking in the latter.