Discrete approach to incoherent excitations in conductors

While keeping the discreteness of the reciprocal space, we calculate the spectrum of incoherent electron-hole excitations in the conducting Fermi liquids. The method is illustrated on the well-known jellium model within the random phase approximation. It also leads to the formulation of a sum rule from which we get the details of the dispersion curve for the collective plasmon mode. The notion of time averaging in the discrete approach is briefly recalled.