Diffusion and correlation in a coherent representation

Using a Fock-space formalism for the Master equation and introducing the density operator we present an unified method to derive kinetic equations for hopping processes with and without exclusion on a lattice. The corresponding Liouvillians are written in terms of Fermi or Bose operators, respectively. Although the Liouvillians are different the averaged particle numbers obey the same diffusion equation. Differences appear in the correlation functions only. The Master equation can be transformed into a differential equation in a coherent state representation. Using the algebraic properties of Grassmann numbers we are able to find the exact statonary solution for diffusion with exclusion. The conductivity can be derived in the bosonic and the fermionic case. The results are in accordance with those obtained with different other methods.