Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state

The Moore-Read Pfaffian $\nu =5\mathrm{/}2$ quantum Hall state is a p-wave super-conductor of composite fermions. Small deviations from $\nu =5\mathrm{/}2$ result in the formation of an array of vortices within this super-conductor, each supporting a Majorana zero mode near its core. Here we consider how tunneling between these cores is reflected in the electronic response to an electric field of non-zero wave vector $\mathbf{q}$ and frequency $\omega$. We find a mechanism for dissipative transport at frequencies below the $\nu =5\mathrm{/}2$ gap, and calculate the $\mathbf{q},\omega$ dependence of the dissipative conductivity. The contributions we find depend exponentially on $\mathrm{\mid }\nu -5\mathrm{/}2{\mathrm{\mid }}^{-1\mathrm{/}2}$.