The Independent-Particle Model

Anton Nikolaev Antonov, Peter Edward Hodgson, Ivan Zh. Petkov

GERASIMOS S. ANAGNOSTATOS

Warren D. Grobman, Marshall Luban

A theoretical study of persistent currents in liquid ${\mathrm{He}}^{4}$ 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 ${\ensuremath{\phi}}_{c}$ with nonzero angular momentum ${l}_{c}$ 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 $T=0$\ifmmode^\circ\else\textdegree\fi{}K. For both models persistent currents are possible at $T=0$ provided that the interactions between particles are sufficiently strong and ${l}_{c}$ does not exceed a characteristic critical value ${l}_{M}$. The quantity ${l}_{M}$ 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 ${\ensuremath{\rho}}_{c}(T)$ of particles macroscopically occupying ${\ensuremath{\phi}}_{c}$ 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.

I.V. Simenog, D.V. Shapoval

We obtain limiting model-independent correlations between the low-energy scattering parameters and the spectrum of three spinless particles which demonstrate the basic features observed in calculations with specific interaction potentials.

Malcolm H. MacGregor