Critical non-thermal fixed point and the dynamical condensation phase transition

This paper investigates whether the equilibrium phase transition of a 3D Bose gas—specifically the Bose-Einstein condensation (BEC) transition—serves as an organizing principle for the system's long-time dynamics following a rapid cooling quench. The authors seek to determine if different post-quench energy states lead to distinct, universal non-equilibrium attractors, effectively establishing a dynamical counterpart to the equilibrium phase diagram.

The researchers employ a non-perturbative quantum kinetic framework to track the spatio-temporal evolution of the momentum distribution of a uniform Bose gas. By solving the kinetic equation, they account for repeated scattering events through a renormalized effective interaction. This approach allows them to regularize the finite-time singularities typically found in standard Boltzmann-based descriptions of turbulence, enabling a reliable analysis of the system's long-time behavior across different quench depths.

The study identifies three universal dynamical regimes separated by the critical momentum $p_c$ associated with the BEC transition:

1. Thermal Fixed Point ($p_0 > p_c$): Quenches that leave the gas in the normal phase exhibit a standard relaxation toward a thermal equilibrium distribution, characterized by the saturation of the zero-momentum occupation.
2. Coarsening Fixed Point ($p_0 < p_c$): Quenches below the threshold trigger an inverse cascade. The system initially enters a transient weak-turbulence regime before crossing over to a long-time coarsening fixed point, where the dynamics are driven by the diffusive recombination of vortex lines and exhibit algebraic growth of the zero-momentum mode.
3. Critical Fixed Point ($p_0 = p_c$): Quenches tuned precisely to the condensation threshold are governed by a distinct critical fixed point. This regime is characterized by the superdiffusive spreading of critical fluctuations and a unique set of dynamical scaling exponents, confirming that the equilibrium critical point also organizes the non-equilibrium dynamics.