Persistent Currents in Many-Boson Systems

A theoretical study of persistent currents in liquid He⁴ is given, in which a system of N interacting bosons confined to a cylindrical container is chosen as a model. It is argued that these currents are metastable and a general model-independent stability criterion valid for all temperatures is derived. In this formulation it is essential that there is a single-particle state φc with nonzero angular momentum lc which is occupied by a macroscopic number [$O(N)$] of particles. The stability criterion is applied to the study of two soluble models, one, an independent-particle model studied for all temperatures, the other a quasiparticle model studied for $T=0$^∘{}K. For both models persistent currents are possible at $T=0$ provided that the interactions between particles are sufficiently strong and lc does not exceed a characteristic critical value lM. The quantity lM is calculated for different choices of single-particle functions, and in particular for the solutions of a Hartree equation, which is relevant to a description of line vortices with quantized circulation. The density ρc(T) of particles macroscopically occupying φc at a temperature T, as well as the critical temperature T* above which no persistent currents are possible, are calculated for the independent-particle model.