Criticality and superfluidity in a dilute Bose fluid

Abstract

The crossover from ideal-Bose-gas behavior to nonclassical, XY-like criticality in a dilute, interacting Bose fluid is considered in detail with emphasis on the superfluid density, ${\rho }_s$(T), below the transition. A general discussion of crossover scaling in constrained systems shows that ${\rho }_s$ and other temperature-dependent thermodynamic functions at controlled overall density can be expressed in terms of universal scaling functions. The finite-temperature Green’s function formalism is used to calculate the associated linear scaling fields and the crossover exponent exactly for all dimensionalities d>2, scaling predictions, including logarithmic singularities just at d=3, being checked via second-order computations. A mapping of the Bose problem onto the classical $s^4$ spin model is achieved which is asymptotically exact in the critical region. In this way, previously known renormalization-group results are used to calculate the scaling functions for ${\rho }_s$, for the off-diagonal susceptibility, etc., to first order in ε=4-d. Good agreement is found with the experimental measurements by Reppy and co-workers of ${\rho }_s$(T) for helium absorbed at low coverages in Vycor glass (of pore size 50–80 Å). An effective-mass ratio $m^{\mathrm{*}}$/m≃1.5, and an effective-scattering-length ratio $a^{\mathrm{*}}$/a≃1.3 are indicated for mobile helium in the Vycor (although the irregular character of Vycor has not, at this point, been fully allowed for in the theory). Other approaches in the literature to computing the critical behavior of quantum-mechanical systems are reviewed and related to the present analysis.