Spin tunnelling in mesoscopic systems

We study spin tunnelling in molecular magnets as an instance of a mesoscopi c phenomenon, with special emphasis on the molecule Fes. We show that the t unnel splitting between various pairs of Zeeman levels in this molecule osc illates as a function of applied magnetic field, vanishing completely at sp ecial points in the space of magnetic fields, known as diabolical points. T his phenomena is explained in terms of two approaches, one based on spin-co herent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for th e diabolical points are obtained for a model Hamiltonian.