Nonequilibrium fixed points in longitudinally expanding scalar theories: infrared cascade, Bose condensation and a challenge for kinetic theory

TL;DR

This paper investigates nonequilibrium fixed points in longitudinally expanding scalar theories, revealing new infrared scaling regimes, Bose-Einstein condensation formation, and challenges for traditional kinetic theory approaches.

Contribution

It identifies two new self-similar regimes in expanding scalar theories, including an IR regime with Bose-Einstein condensation, and develops an effective vertex-resummed kinetic theory.

Findings

IR regime leads to Bose-Einstein Condensation

Universal IR scaling exponents characterized by large-N expansion

Infrared dynamics challenge conventional kinetic theory

Abstract

In Phys. Rev. Lett. 114 (2015) 6, 061601, we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and $N$-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of a Bose-Einstein Condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-$N$ expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. We argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.