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 [1]. 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 simulations of 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 [2], providing new insights into the intricate dynamics of the AB transition.

[1] QUEST-DMC collaboration, M. Hindmarsh et al, J. Low Temp Phys 215, 495–524, (2024).

[2] QUEST-DMC collaboration, P.J. Heikkinen et al, J. Low Temp Phys 215, 477–494, (2024).