Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of ${}^{4}\mathrm{He}$ atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of ${}^{4}\mathrm{He}$ atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.

arXiv:cond-mat/0201281Physical Review AFeb 28, 200354 citations

Self-consistent approximations to non-equilibrium many-body theory

Yu. B. Ivanov, Jörn Knoll, Dmitry N. Voskresensky

arXiv:hep-ph/9807351Nuclear Physics AOct 1, 1999104 citations

Lectures on the many-body problem in nuclear physics

L. Rosenfeld, J. Bro-Jørgensen, A. Haatuft +1 more

NORDITA (Nordisk institut for teoretisk atomfysik) eBooksJan 1, 19590 citations

Reformulation of Coupled-Cluster Theory for Many-Fermion System on Similarity-Transformation Theory

Kenji Suzuki

It is shown that the coupled-cluster theory can be interpreted as an application of the similarity-transformation theory for the quantum-mechanical eigenvalue problem. The transformed Hamiltonian H = e-THeT is introduced with the cluster operator T. The Hamiltonian H is expanded into different clusters according to the number of interacting particles. The n-body part of the cluster operator T is determined from the condition that the n-body part of H should be decoupled between two n-body states with configurations of n occupied and n unoccupied orbits. It is proved that the problem of solving the decoupling equation can be reduced to solving an eigenvalue equation for a subsystem Hamiltonian. it is also proved that there exist one- and two-body subsystem equations with certain one- and two-body average fields such that they determine the one- and two-body parts of the cluster operator and consequently lead to the exact ground-state energy.It is shown that the coupled-cluster theory can be interpreted as an application of the similarity-transformation theory for the quantum-mechanical eigenvalue problem. The transformed Hamiltonian H = e-THeT is introduced with the cluster operator T. The Hamiltonian H is expanded into different clusters according to the number of interacting particles. The n-body part of the cluster operator T is determined from the condition that the n-body part of H should be decoupled between two n-body states with configurations of n occupied and n unoccupied orbits. It is proved that the problem of solving the decoupling equation can be reduced to solving an eigenvalue equation for a subsystem Hamiltonian. it is also proved that there exist one- and two-body subsystem equations with certain one- and two-body average fields such that they determine the one- and two-body parts of the cluster operator and consequently lead to the exact ground-state energy.

Progress of Theoretical PhysicsApr 1, 19929 citations

Problems in Theory of Many-Body Systems.

James Woods Halley

Jan 1, 19650 citations

Connections between many-body perturbation and coupled-cluster theories

Raúl Quintero-Monsebaiz, Enzo Monino, Antoine Marie +1 more

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe–Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe–Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe–Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe–Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.

arXiv:2210.07043The Journal of Chemical PhysicsNov 28, 202228 citations

{}^{4}\mathrm{He}

atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.