Problems in Theory of Many-Body Systems.

W E Turner et al. New York: Benjamin 1969 pp vii + 265, price £2 The Institute of Physics and The Physical Society has decided to have republished selected articles, with a common theme, from Reports on Progress in Physics . The present volume on many-body problems is such a venture and contains reviews entitled 'Green functions in statistical mechanics' (Parry and Turner 1964), 'Theory and applications of the density matrix' (ter Haar 1961), 'The equation of state of dense systems' (Rowlinson 1965), 'The theory of irreversible processes' (Chester 1963), 'Quantum theory of many-body systems' (Hugenholtz 1965) and 'The fluctuation-dissipation theorem' (Kubo 1966).W E Turner et al. New York: Benjamin 1969 pp vii + 265, price £2 The Institute of Physics and The Physical Society has decided to have republished selected articles, with a common theme, from Reports on Progress in Physics . The present volume on many-body problems is such a venture and contains reviews entitled 'Green functions in statistical mechanics' (Parry and Turner 1964), 'Theory and applications of the density matrix' (ter Haar 1961), 'The equation of state of dense systems' (Rowlinson 1965), 'The theory of irreversible processes' (Chester 1963), 'Quantum theory of many-body systems' (Hugenholtz 1965) and 'The fluctuation-dissipation theorem' (Kubo 1966).

Physics BulletinJan 1, 19701 citation

Some recent developments in the many-body problem

D. ter Haar

Summary A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.Summary A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.

Contemporary PhysicsDec 1, 19593 citations

Lectures on the Many-body Problems

Elsevier eBooksJan 1, 196439 citations

Lectures on the many-body problem

S. Takagi, S.B. Khadkikar

Tata Institute of Fundamental Research eBooksJan 1, 19630 citations

Using classical many-body structure to determine electronic structure: An approach using k -electron distribution functions

Paul W. Ayers

The quantum $N$ -electron structure problem is expressed as a classical $N$ -body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using $k$ -electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory $(k=1)$ and pair density-functional theory $(k=2)$ and culminating in an exact treatment of the entire $N$ -electron system $(k=N)$ .The quantum $N$-electron structure problem is expressed as a classical $N$-body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using $k$-electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory $(k=1)$ and pair density-functional theory $(k=2)$ and culminating in an exact treatment of the entire $N$-electron system $(k=N)$.

Physical Review AOct 3, 200644 citations

The quantum

N

-electron structure problem is expressed as a classical

N

-body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using

k

-electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory

(k=1)

and pair density-functional theory

(k=2)

and culminating in an exact treatment of the entire

N

-electron system

(k=N)