On the calculation of the density of localized states in a dense fluid

The authors report a theoretical analysis of the density of localized states in a fluid. The basic mathematical technique employed is the conversion of partially summed, infinite order, perturbation theory to integral equation representation. Two integral equation approximations to the renormalized perturbation series for the one electron two site Green function of an offdiagonal disordered system are developed. These treat the radial disorder in a realistic although not exact, fashion. The integral equations themselves have a structure analogous to that of the successful Percus-Yevick and Hypernetted Chain approximate theories of the pair distribution function of a simple liquid. Numerical calculations which delineate the properties of the integral equations developed are also reported. The numerical calculations show the existence of localized states below a critical energy and are consistent with the predictions from much simpler lattice models of disordered systems.