  Aharonov-Bohm Physics at the two-particle level is investigated for
distinguishable interacting charged particles through the exact solution of a
toy model with confined states. The effect of the inaccessible magnetic flux is
distributed between the center-of-mass and the internal pair level, and the
nontrivial manner in which the two levels are mutually affecting each other
demonstrates the interplay between interactions, nontrivial topology, the
Aharonov-Bohm flux and the characteristics of a charged quantal mixture.
Analytical expressions for energy spectra, wavefunctions, (flux-dependent)
critical interactions for binding and current densities are derived, and these
offer the rare possibility to study persistent currents from the point of view
of an interacting nanoscopic system. Two cyclic adiabatic processes are
identified, one coupled to the center-of-mass behavior and the other defined on
the two-body interaction potential, with the associated Berry's phases also
analytically determined; these are found to be directly linked to the electric
and probability (persistent) currents in nontrivial ways that are shown to be
universal (independent of the actual form of the interaction). The direct
connection of the two-body Berry's phase to the electric current for a neutral
system is found to disappear in case of identical particles - hence revealing
the character of a charged mixture as being crucial for exhibiting these
universal behaviors.
