A correlation estimate with applications to quantum systems with Coulomb interactions. (English) Zbl 0843.47041

Graf, Gian Michele; Solovej, Jan Philip

Rev. Math. Phys. 6, No. 5a, 977-997 (1994).

Summary: We consider some two-body operators acting on a Fock space with either fermionic or no statistics. We prove that they are bounded below by one-body operators which mimic exchange effects. This allows us to compare two-body correlations of fermionic and bosonic systems with those in Hartree-Fock, respectively Hartree theory. Applications of the fermionic estimate yield lower bounds for the ground state energy of jellium at high densities and of molecules with large nuclear charges.

MSC:

47N50	Applications of operator theory in the physical sciences
81U05	\(2\)-body potential quantum scattering theory
81V10	Electromagnetic interaction; quantum electrodynamics

Keywords:

two-body operators acting on a Fock space with either fermionic or no statistics; one-body operators; exchange effects; two-body correlations of fermionic and bosonic systems; Hartree-Fock; Hartree theory; ground state energy of jellium at high densities; molecules with large nuclear charges