Aharonov-Bohm effects in entangled molecules

Molecules which are magnetic and conducting, if suitably entangled (e.g., catenanes and knots) could exhibit Aharonov-Bohm effects which can be viewed as particular examples of a Berry phase. The corrections to the quantum energy levels reflect the entangled geometry of the molecules and, while small (they are proportional to the square of the fine structure constant), may be observable. We illustrate these corrections for a number of catenated and knotted structures. For couplings between the components of a catenane (link), the Aharonov-Bohm corrections are determined by integer-valued linking numbers. For knots, the Aharonov-Bohm correction is proportional to the geometric writhe of the knot.