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Nonequilibrium Greens functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Greens functions formalism to the dynamics of central nuclear reactions. As the first step, mean-field evolution for the density matrix for colliding slabs is studied in one dimension. The strategy to extend the dynamics to correlations is described.
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Linear response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions with conserving self-energy insertions, thereby satisfying the energy-sum rule. Nucleons are regarded as moving in a mean field defined by an effective mass. A two-body effective (or residual) interaction, represented by a gaussian local interaction, is used to find the effect of correlations in a second order as well as a ring approximation. The response function S(e,q) is calculated for 0.2<q<1.2 fm^{-1}. Comparison is made with the nucleons being un-correlated, RPA+HF only.
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while $2^{nd}$ order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian it local rm potential. We present numerical results for the response function $S(omega,q_0)$ for $q_0=0.2,0.4$ and $0.8 {rm fm}^{-1}$. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the HF+RPA approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sjoberg and followers using methods developped by Babu and Brown, with special emphasis on the induced interaction.
I review the application of self-consistent Greens functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of extrapolation methods from finite to zero temperature, have allowed for realistic predictions of the equation of state of infinite symmetric, asymmetric and neutron matter based on chiral interactions. Microscopic properties, like momentum distributions or spectral functions, are also accessible. Using an indicative set of results based on a subset of chiral interactions, I summarise here the first-principles description of infinite nuclear system provided by Greens functions techniques, in the context of several issues of relevance for nuclear theory including, but not limited to, the role of short-range correlations in nuclear systems, nuclear phase transitions and the isospin dependence of nuclear observables.
Basic issues of the time-dependent density-functional theory are discussed, especially on the real-time calculation of the linear response functions. Some remarks on the derivation of the time-dependent Kohn-Sham equations and on the numerical methods are given.
We present calculations for symmetric nuclear matter using chiral nuclear interactions within the Self-Consistent Greens Functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlying dependence on the SRG evolution scale.
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