Trapped Second Sound Waves on a Nonequilibrium Superfluid-Normal Interface

Abstract

When a heat current $Q$ is driven through a near-critical sample of ${}^{4}\mathrm{He}$ a situation may be realized in which a nonequilibrium superfluid-normal interface appears. We derive the effective two-dimensional dynamics of this interface, showing that a surface sound mode exists whose amplitude decays exponentially into the bulk on either side. These modes are singularly damped, with $D(q)\ensuremath{\propto}{q}^{3/2}$ rather than ${q}^{2}$. We find that thermal fluctuations do not roughen the interface, thus aiding the DYNAMX microgravity experiment which proposes to measure its detailed properties.