Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium

Area of Science:

• Quantum Field Theory
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Nonthermal fixed points describe universal scaling in quantum systems far from equilibrium.
• Understanding the dynamics of perturbations around these points is crucial for emergent phenomena.

Purpose of the Study:

• Investigate the stability of perturbations around nonthermal fixed points in quantum many-body systems.
• Determine the scaling exponents governing these dynamics using theoretical methods.

Main Methods:

• Employed a self-consistent large-N expansion to next-to-leading order for an N-component scalar quantum field theory in 3+1 dimensions.
• Utilized spectral function computations to identify quasiparticle states and their dispersion relations.
• Applied linear response theory to analyze the competition between scattering processes.

Main Results:

• Identified both stable and unstable perturbations, with unstable ones causing quasiexponential deviations.
• Revealed a tower of far-from-equilibrium quasiparticle states and their dispersion relations.
• Demonstrated that unstable dynamics result from elastic scattering competition.

Conclusions:

• Introduced the concept of "scaling instability" as the mechanism for infrared attraction.
• Explained emergent stability through a universal scaling of the unstable regime via quasiparticle cascades.
• Provided an ab initio understanding of stability in self-organized scaling phenomena.