Numerical simulations of superfluid 3He

The first-order phase transition between the supercooled A- and B-phase in superfluid 3He at millikelvin temperatures remains a long-standing puzzle. While homogeneous nucleation (HN) theory predicts an almost negligible transition rate, experiments observe A-phase lifetimes ranging from hours to days, indicating a highly non-equilibrium process. Various mechanisms,including the “baked-Alaska” model and the “cosmological” scenario, have been proposed to explain this discrepancy, with broader implications for cosmological phase transitions and dark matter models. Recent experiments have revealed new properties of this transition, emphasizing the need to understand the superfluid phase seeding, the post-seeding evolution of the order parameter and the influence of container boundaries on A-phase stability. To address this challenge, we present dyGiLa, a massively parallel code for lattice simulationsof superfluid 3He. Built using computational techniques originally developed for cosmological field theory simulations, dyGiLa solves the effective field theory of the superfluid order parameter by integrating the time-dependent Ginzburg-Landau equations on large-scale cuboidal grids, constrained only by available computational resources. This transfer of technology from cosmology enables efficient and scalable simulations of complex non-equilibrium dynamics in p-wave superfluid 3He. We demonstrate results from rapid quench simulations, showcasing the emergence of diverse topological defects and phase boundaries. DyGiLa is currently being employed to interpret experimental findings from the QUEST-DMC collaboration, providing new insights into the intricate dynamics of the AB transition.