Abstract We modify the nonequilibrium Keldysh diagram technique to systematically account for non-Gaussian initial correlations. We represent information about the initial state of the system as an additional term in the Keldysh action, which is expressed in terms of the cumulants of the initial Wigner functional. This additional term leads to the appearance of additional vertices in the diagram technique. We study the role of non-Gaussian initial correlations in the further evolution of correlation functions. In particular, we show that the presence of non-Gaussian correlations of odd order leads to the generation of a mean field. We obtain Dyson equations with partially resummed self-energies and prove that diagrams with a finite number of loops contain a finite number of non-Gaussian cumulants of the initial Wigner functional. We apply the modified diagram technique to the description of the evolution of a scalar field after a quench and show that in the limit of short interaction times this technique leads to exact results.
We study theoretically the quasiparticle lifetime, due to Coulomb scattering, in a two-dimensional electron system. It has long been established that in the limit of low excitation energy and temperature, the inverse lifetime behaves as ${\mathrm{\ensuremath{\tau}}}_{\mathrm{ee}}^{\mathrm{\ensuremath{-}}1}$(p)\ensuremath{\propto}(\ensuremath{\Delta}/${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$
)2ln(${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$/\ensuremath{\Delta}), where \ensuremath{\Delta}\ensuremath{\equiv}max(|${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$|,
kBT). This result has been obtained in the leading order of the Coulomb interaction. We show that higher-order terms in the interaction contribute higher-order logarithmic factors, meaning that a correct theory must sum up all orders of the interaction. After performing this summation, using the Keldysh diagram technique, we find that the renormalized lifetime still has the same general form as above. On the other hand we find that only forward scattering contributes to the lifetime, whereas, in leading-order theory, both forward and backward scattering make a contribution (a similar result has already been obtained for the two-dimensional Hubbard model). This leads to a different proportionality constant for the lifetime. Because we employ the Keldysh diagram technique, we are also able to give an expression for the collision operator, which can be used in the study of near-equilibrium processes. \textcopyright{} 1996 The American Physical Society.