Superfluid transition temperature from the Lindemann-like criterion

Abstract

We further analyze the recently proposed criterion, according to which a superfluid transition occurs whenever the r.m.s. displacement of a particle from its initial position in imaginary time reaches a certain fraction of the interparticle distance. The critical temperature $T_\lambda$ is expressed in terms of the single particle mobility. Within the Drude approximation for the mobility $T_\lambda$ is determined by the friction coefficient (or by the viscosity for dense liquids). To check the validity of the criterion the resulting formula is applied to non-ideal Bose gas, to liquid helium and to $^3$He-$^4$He mixtures. A reasonable qualitative agreement with available experiments is obtained in all cases. In the case of the Bose gas the present approach results also in an upper bound on the peak value of $T_{\lambda}/T_{\lambda}^0$, where $T_{\lambda}^0$ is the critical temperature for the ideal gas.