Universal dynamics on the way to thermalization

Abstract

It is demonstrated how a many-body system far from thermal equilibrium can exhibit universal dynamics in passing a nonthermal fixed point. As an example, the process of Bose-Einstein (BE) condensation of a dilute cold gas is considered. If the particle flux into the low-energy modes, induced, for example by a cooling quench, is sufficiently strong, the Bose gas develops a characteristic power-law single-particle spectrum ∼ − n k k ( ) 5 , and critical slowing down in time occurs. The fixed point is shown to be marked by the creation and dilution of tangled vortex lines. Alternatively, for a weak cooling quench and particle flux, the condensation process runs quasi-adiabatically, passing by the fixed point in the far distance, and the signatures of critical scaling remain absent.

Universality Far from Equilibrium: From Superfluid Bose Gases to Heavy-Ion Collisions

“…We conclude that the very high occupancies at low-momenta enhance scattering rates to overcome the rate of longitudinal expansion. The situation is very similar to non-expanding systems, where a nonthermal infrared fixed point was observed previously for scalar field theories [3][4][5][6][7][8]18]. In particular, the scaling behavior agrees with the inverse particle cascade found in non-relativistic Bose gases without expansion, where the observed scaling exponent characterizes superfluid turbulence in three spatial dimensions [5][6][7][8].…”

“…For non-expanding scalar theories, the nonthermal infrared fixed point catalyzes the formation of a BoseEinstein condensate [7,8,23]. We repeat the corresponding analysis in the case of longitudinal expansion and search for a scalar-field zero-mode which scales with volume, namely, F (p = 0; t) ∼ V .…”

“…Because of the large typical occupancies, the system is strongly correlated and its properties become insensitive to the details of the underlying model or initial conditions. The far-from-equilibrium behavior can be described in terms of universal exponents and scaling functions [3][4][5][6][7][8], similar to the description of critical phenomena in thermal equilibrium.…”

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

“…Another possible reason includes a change of the underlying dynamics, for example, from a perturbative to a nonperturbative mechanism below a characteristic momentum scale. In the context of wave turbulence, each momentum region is usually referred to as an inertial range of momenta, with various examples provided in the literature [20,27,28,36,69,[89][90][91][92].…”

“…This results from the condensation behavior F 0 ∼ t 3/2 , a consequence of the inverse particle cascade from the low momentum region that populates the zero mode [91][92][93][94][95].…”