Critical dynamics of the superfluid phase transition in Model F

TL;DR

This paper presents numerical simulations of the critical dynamics near the superfluid phase transition using model F, confirming expected dynamical exponents and observing second sound mode emergence.

Contribution

It implements a stochastic hydrodynamic simulation of model F to study superfluid critical dynamics, including the dynamical exponent and second sound behavior.

Findings

Dynamical exponent z ≈ 3/2 observed

Emergence of propagating second sound mode

Second sound diffusivity scales with correlation length as D_s ∼ ξ^{1/2}

Abstract

We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and Halperin. This theory is expected to describe dynamic scaling near the lambda transition in liquid $^4$He, Bose-Einstein condensation in ultracold atomic gases, and the superfluid transition in the unitary Fermi gas. Our simulation is based on a Metropolis algorithm previously applied to the critical endpoint of the liquid-gas phase transition in ordinary fluids. In the model E truncation of model F we obtain the expected dynamical exponent $z\simeq 3/2$. We observe the emergence of a propagating second sound mode at the phase transition. The second sound diffusivity $D_s$ is consistent with the scaling relation $D_s\sim \xi^{x_\kappa}$, where $\xi$ is the correlation length and $x_\kappa=1/2$.