Towards a nonequilibrium Green's function description of nuclear reactions: one-dimensional mean-field dynamics

TL;DR

This paper develops a Green's function methodology for simulating one-dimensional nuclear reactions within the mean-field approximation, focusing on initial state preparation and the significance of far-off-diagonal matrix elements.

Contribution

It introduces practical techniques for initial state preparation and matrix element suppression in Green's function simulations of nuclear reactions.

Findings

Far-away Green's function matrix elements are less important due to system expansion.

Erasing off-diagonal elements corresponds to averaging in momentum space.

Methodology enables consistent description of quantum many-body nuclear dynamics.

Abstract

Nonequilibrium Green's function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green's function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green's function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied to system expansion. We also examine the evolution of the Wigner function and verify quantitatively that erasing of the off-diagonal elements corresponds to averaging out of the momentum-space details in the Wigner function.