Pseudopotential method and dilute hard “sphere” Bose gas in dimensions 2, 4 and 5

D. G. Friend

A. Isihara, D. D. H. Yee

X.-Z. Wang

D. G. Friend, Richard David Etters

Chen Ning Yang

The ground-state energy for a dilute hard sphere Bose gas in various dimensions is studied theoretically through the pseudopotential method. Earlier analysis has not been mathematically rigorous so the current treatment uses new technologies and powerful computers. The 1D and 2D systems have been studied experimentally and qualitative and quantitative features exhibited for these and other dimensions.

Toshio Soda

The impurity excitation spectrum is calculated for the hard-sphere Bose gas with dilute impurity concentration, using the pseudopotential method of Lee, Huang, and Yang. The spectrum for the ideal case, in which the mass and interaction of impurity are the same with those of the bosons in the gas, is k2 in the unit of 2ma = h/ = 1 (ma being the mass of boson, and k the momentum of impurity), with an effective mass correction of −6445[(ρa3)12/π12]k2+O[(ρa3)k2,k4], where ρ is the density of the boson gas, and a is the hard-sphere diameter of the boson. The general impurity case is also calculated and found to have an impurity spectrum rk2, with a similar effective mass correction, where r is the mass ratio of the boson to the impurity.