Quantum theory of interacting bosons

Abstract

Some qualitative features of the ground state of a system of interacting bosons are discussed using wave functions suggested by the semiclassical theory of boson wave fields. For the case where one deals with weak repulsions, one is lead to a variational extension of Bogolyubov's work. A finite fraction of the N particles occupies the zero momentum single particle state, and the dynamic correlations are described by pair excitations. When attractive forces play a decisive role, two cases are found. In one case a finite fraction of the particles occupies a single particle state, which is now periodic in space. The dynamic correlations are described as a generalization of pair excitations which is different in character for excitation momenta of the order of the inverse of the range of the attractive forces. The single particle state and dynamic correlations are codetermined in a systematic way. The approximate ground state shows long range order which is destroyed at finite temperatures. A second case where attractions are important is the solid state of the boson system. The ground state has the property that of the order of N orthogonal single particle states are occupied, each with an average of approximately one particle.