Low lying electronic tail spectrum of the attractive δ-potential random system by the path integral method and coherent state representation variational method

Abstract

By using the path integral method to study the “partition function” and therefore the density of states of the attractive Frisch-Lloyd random system, it is found that the “partition function” is divergent. Therefore, we modify the Frisch-Lloyd model to a system with regular lattice sites on which the atoms are randomly distributed. Path integral and coherent state representation variational methods are applied to this random system; by using the effective Hamiltonian theory of a periodic potential with slowly varying envelope, the low lying tail spectrum which is consistent with the Lifshitz conjecture for a random system is obtained.