Excitation of Collective Modes in a Chiral Condensate by a Thermal Quench

Rapid cooling through the 2nd-order phase transition into chiral superfluid ³He-A excites collective excitations, in addition to topological defects that are formed via the Kibble-Zurek mechanism. Order parameter fluctuations are projected onto the four collective excitations of ³He-A: Higgs (M = 2Δ), Goldstone (M = 0), and two degenerate clapping modes (M = 2^1/2 Δ), each with dispersion ε(q) = (M² + c²q²)^1/2. Weakly damped quench simulations based on time-dependent Ginzburg-Landau theory with Gaussian space-time white noise generate a highly excited inhomogenous condensate that relaxes into a lower energy configuration. In large scale simulations, there is a complex network of domain walls and vortices. We describe the temporal evolution and coarsening dynamics in terms of Fourier modes. In the case of a topological-defect-free system, the Fourier modes following a quench are shown to decay until they reach a steady state value, where the noise process imprints a 1/f power spectral density (PSD) on each of the four excitation modes. We also discuss a mechanism for the rapid growth of Fourier modes near the Kibble-Zurek freeze-out time.