Some Nonequilibrium Properties of a Bose System of Hard Spheres at Extremely Low Temperatures

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Abstract
The pseudopotential method is used to study a special type of flow for a Bose system of hard spheres. In the first‐order approximation, the wave function of the entire system is assumed to be the product of identical single‐particle wave functions, which in general are time‐dependent. Such a flow is necessarily irrotational, and the single‐particle wave function satisfies a Schrödinger equation with a nonlinear self‐coupling term. On the basis of this equation of motion, the following properties of the Bose system are discussed: the effect of the rigid wall, the moment of inertia, the compressional wave, and a type of ``vortex filament.'' In the second‐order approximation, the wave function of the system is expressed in terms of two functions such that one of them describes the single‐particle state suitable for most of the particles while the other one describes the pair excitations. The much more complicated equations of motion are found, but in this approximation the flow is no longer strictly irrotational. The compressional waves are also studied in the second‐order approximation.