Abstract
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's 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 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 works by Bozek et al. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while 2nd order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian local potential.We show results of calculations of the response function S(ɷ,q0) for q0 = 0.2, 0.4 and 0.8fm-1. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included.We discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Babu and Brown and followers.
Highlights
Response functions, the response of a many-body system to an external perturbation is instrumental in our understanding of the properties and interactions involved in the excitations of the system
This report concerns the calculation of linear density response functions for symmetric nuclear matter
It was shown by Baym and Kadanoff [5] that, if one wishes to construct the linear response function with dressed equilibrium Green’s functions, appropriate vertex corrections to the polarization bubble are necessary to guarantee the preservation of the local continuity equation for the particle density and current in the excited system, which in turn implies the satisfaction of the energy-weighted sum-rule
Summary
The response of a many-body system to an external perturbation is instrumental in our understanding of the properties and interactions involved in the excitations of the system. Of particular interest here is the effect of correlations i.e. dressed propagators and collision-terms It was shown by Baym and Kadanoff [5] that, if one wishes to construct the linear response function with dressed equilibrium Green’s functions, appropriate vertex corrections to the polarization bubble are necessary to guarantee the preservation of the local continuity equation for the particle density and current in the excited system, which in turn implies the satisfaction of the energy-weighted sum-rule. This problem has traditionally involved solving a Bethe-Salpeter equation to calculate these vertex corrections. A diagrammatic representation of the main equations is shown in an Appendix
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