Nonuniform states of an imperfect bose gas

Abstract

The low-lying states of an inhomogeneous weakly interacting Bose gas are investigated with the Bogoliubov transformation. The particle density n(r), the particle current j(r), and the pair density function n 2(r, r′) are evaluated at finite temperature T, including both condensate and noncondensate contributions. For a uniformly moving condensate, j is proportional to the Landau superfluid density ϱ s ( T). For a singly quantized vortex with core radius ξ, the asymptotic properties ( r → ∞) are given by n( r) ∼ n [1 + O( ξ 2 r 2 )] and j θ(r) ∼ ( n h ̵ mr )[1 + O( ξ 2 r 2 )] , where n = n 0 + n′ is the total density (condensate plus noncondensate) in a uniform system. Near the axis of the vortex, n(0) = n′(0) is estimated to be ≈ 1.4 n′, yet j θ ( r) vanishes linearly, implying a finite kinetic energy density in the core. The N-body wave function in configuration space is constructed for the lowest state of a vortex. It suggests an improved form of the trial function used by Chester, Metz, and Reatto for a vortex in 4He.