Quasi-particle excitations and the many-boson problem

Abstract

A many-boson theory is developed that is applicable to systems with intermediate as well as weak coupling strength. A transformation of basis from the single particle representation to that of an independent collection of quasi-particles, which represent the normal modes of the system, is accomplished in an approximate way. The results are in the form of coupled, nonlinear, integral equations for the ground state energy, the excitation energy, the quasi-particle excitation operator, and the momentum distribution function. No a priori assumptions concerning the population in any single low-lying momentum state is required nor is any artificial separation of the single particle zero-momentum state from states of higher momentum necessary. Contact with the results of weak-coupling theories is established by imposing additional restrictions on the interaction potential and on the momentum distribution of particles. It is shown that the weak-coupling equations are valid under more general circumstances than was previously apparent. A general theorem is provided for which the existence of a zero in the excitation spectrum at zero-momentum is required. It is also shown that the low-lying excitations follow a dispersion rule that is linear in momentum, independent of the form of the interaction. The theory is applied to the charged boson gas and, for the case where the zero-momentum state is appreciably depleted, the resulting excitation spectrum is quite different at low momentum from that derived in previous calculations.