Application of field-theoretic, collective-coordinate, and correlated-basis-function methods to many-boson systems

Abstract

The collective-coordinate and correlated-basis-function approaches are systematically applied to the determination of the elementary excitation spectrum $\ensuremath{\omega}(k)$ and the static structure function $S(k)$ for two models of a Bose gas which can be characterized by a single small expansion parameter $g$. Results are obtained to first order in $g$, the leading order in which multiexcitation processes are present, and are compared with those found by the microscopic-dielectric-function approach. It is found that a collective-coordinate calculation of $\ensuremath{\omega}(k)$ by Sunakawa, Yamasaki, and Kebukawa is incomplete to first order in $g$ and that the convolution approximation for the three-particle distribution function in the correlated-basis-function formalism leads to incorrect results for overlap matrix element and for $S(k)$. A form for the overlap matrix element is proposed which leads to correct first-order results. Various properties of $\ensuremath{\omega}(k)$, $S(k)$, and the dynamic structure function are discussed.