A conserving approximation evaluation of superfluid density within the pair theory of superfluids

Abstract

The evaluation of the superfluid density, defined by the weak field response of the system, within the pairing theory of “pure” superfluids of Fermi or Bose statistics is considered. The need for evaluating this within what Baym and Kadanoff term a conserving approximation is emphasized. A formalism for generating manifestly conserving response kernels by analytic continuation at finite temperatures is developed and applied to the problem in question. At zero temperatures this is equivalent to the work of Nambu and others. The superfluid density is obtained in terms of the solution of a linear integral equation, the kernel and inhomogeneous term of which depends on the self-consistent equilibrium solution to the pair model. It is shown in general that this superfluid density tends to the full density at the absolute zero and vanishes above the critical temperature. Finally, some numerical work on the Bose superfluid is presented which is an extension of the calculations of Evans and Imry in the sense that a pseudopotential that more closely parameterizes the dispersion spectrum in He II is employed and that the superfluid density is evaluated as a function of temperature.