  We study the spectrum of off-diagonal fluctuations between displaced fuzzy
spheres in the BMN plane wave matrix model. The displacement is along the plane
of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles
classical tachyons develop and that the spectrum of these modes can be computed
analytically. These tachyons can be related to the familiar Nielsen-Olesen
instabilities in Yang-Mills theory on a constant magnetic background. Many
features of the problem become more apparent when we compare with maximally
supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We
also set up a simple oscillatory trajectory on the displacement between the
fuzzy spheres and study the dynamics of the modes as they become tachyonic for
part of the oscillations. We speculate on their role regarding the possible
thermalization of the system.
