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Register a new userGreens functions techniques for extended nuclear systems
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Authors
A. Rios
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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.
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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.
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.
An approach is outline to constructing an optical potential that includes the effects of antisymmetry and target recoil. it is based on the retarded Greens function, which could make it a better starting point for applications to direct nuclear reactions, particularly when extended to coupled channels. Its form retains a simple connection to folding potentials, even in the presence of three-body forces.
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Greens functions point of view, including two-body and three-body chiral forces. An extended self-consistent Greens function formalism is defined to consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force corresponds to the use of an in-medium propagator in the average which takes into account the correlations characterizing the system at each stage of the many-body calculation. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sumrule to correctly account for the effect of three-body forces. Microscopic as well as macroscopic properties of symmetric nuclear and pure neutron matter are analyzed in detailed.
This paper is devoted to establishing the uniform estimates and asymptotic behaviors of the Greens functions $(G_varepsilon,Pi_varepsilon)$ (and fundamental solutions $(Gamma_varepsilon, Q_varepsilon)$) for the Stokes system with periodically oscillating coefficients (including a system of linear incompressible elasticity). Particular emphasis will be placed on the new oscillation estimates for the pressure component $Pi_varepsilon$. Also, for the first time we prove the textit{adjustable} uniform estimates (i.e., Lipschitz estimate for velocity and oscillation estimate for pressure) by making full use of the Greens functions. Via these estimates, we establish the asymptotic expansions of $G_varepsilon, abla G_varepsilon, Pi_varepsilon$ and more, with a tiny loss on the errors. Some estimates obtained in this paper are new even for Stokes system with constant coefficients, and possess potential applications in homogenization of Stokes or elasticity system.
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