Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

arXiv:1801.09977SciPost PhysicsApr 1, 201922 citations

Semi-classical theory of nuclear reactions

J.R. Rook

Physics Letters BJan 1, 19742 citations

Comparing many-body approaches against the helium atom exact solution

Jing Li, Drummond, Neil David, Peter Schuck +1 more

Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.

Apr 1, 201917 citations

Statistical Theory of the Many-Body Nuclear System

Arturo De Pace, Alfredo Molinari

arXiv:nucl-th/0110056Annals of PhysicsMar 1, 20023 citations

Universal corrections to reaction-diffusion dynamics above the upper critical dimension

Johannes Hofmann

Reaction-diffusion models are common in many areas of statistical physics, where they describe the universal late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, we consider corrections to the late-time scaling above the upper critical dimension, where mean-field theory sets the leading order. We establish that the leading corrections are not given by a small renormalization of the reaction rate due to memory effects, but instead set by higher-order correlation functions that capture memory effects of sub-clusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, we compute these corrections exactly for various $k$ -particle annihilation processes $k A \to \emptyset$ with $k>2$ .Reaction-diffusion models are common in many areas of statistical physics, where they describe the universal late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, we consider corrections to the late-time scaling above the upper critical dimension, where mean-field theory sets the leading order. We establish that the leading corrections are not given by a small renormalization of the reaction rate due to memory effects, but instead set by higher-order correlation functions that capture memory effects of sub-clusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, we compute these corrections exactly for various $k$-particle annihilation processes $k A \to \emptyset$ with $k>2$.

Jun 1, 20210 citations

Theory of Nuclear Reactions and the Many-Body Problem

G.M. Vagradov

Springer eBooksJan 1, 19660 citations

k

-particle annihilation processes

k A \to \emptyset

with

k>2