Superfluid transition in a finite geometry: critical ultrasonics

Abstract

The suppression of order-parameter fluctuations at the boundaries causes the ultrasonic attenuation near the superfluid transition to be lowered below the bulk value. For a confining length L, there are three characteristic lengths in the problem at a given reduced temperature t and given frequency ω. These are the correlation length ξ, the confining length L, and a dynamic length l_d=(2Γ₀/ω)^1/z, where z is the dynamic scaling exponent and Γ₀ is a constant. The attenuation is a function of the two scaled variables ξ/l_d and ld/L. We show that for ξ»l_d, the attenuation per wavelength can be processed in a manner that the data for different ω and L will collapse on a scaling plot as a function of l_d/L. For finite values of L/l_d we exhibit how the data can be plotted as a function of ξ/l_d for different values of ξ/L. We present detailed calculation for temperatures above the bulk transition temperature. These can be tested in future experiments.