Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium

Abstract:

We study the dynamics of perturbations around nonthermal fixed points associated with universal scaling phenomena in quantum many-body systems far from equilibrium. For an $N$-component scalar quantum field theory in $3+1$ space-time dimensions, we determine the stability scaling exponents using a self-consistent large-$N$ expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasiexponential deviations from the fixed point in the infrared. We identify a tower of far-from-equilibrium quasiparticle states and their dispersion relations by computing the spectral function. With the help of linear response theory, we demonstrate that unstable dynamics arises from a competition between elastic scattering processes among the quasiparticle states. What ultimately renders the fixed point dynamically attractive is the phenomenon of a “scaling instability,” which is the universal scaling of the unstable regime toward the infrared due to a self-similar quasiparticle cascade. Our results provide ab initio understanding of emergent stability properties in self-organized scaling phenomena.

T. Preis, M. P. Heller, J. Berges, “Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium”, Phys. Rev. Lett. 130, 031602 (2023).

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.031602

Related to Project A01, A03, A04, A05, B04