We compare the low eigenvalue spectra of the Overlap Dirac operator on sets of dynamical configurations at $\mu_I/mu_I^c$ = 0.5, 1.5, 3 and 4. These were generated with dynamical staggered fermions on $24^3 \times 6$ lattices with a tree-level Symanzik improved gauge action and a staggered Fermion sea quark action with two stout smearing steps and for a quark mass tuned to have the physical pion mass. We find very small changes in the number of zero modes and low lying modes across the chiral transition which is in stark contrast with those across the corresponding finite temperature phases where one sees a drop across it. Possible consequences are discussed.

Nonzero Temperature and Density