Thermalization in weakly coupled nonabelian plasmas

Abstract

We investigate how relativistic, nonabelian plasmas approach equilibrium in a general context. Our treatment is entirely parametric and for small Yang-Mills coupling α. First we study isotropic systems with an initially nonequilibrium momentum distribution. We consider both the case of initially very high occupancy and initially very low occupancy. Then we consider systems which are anisotropic. We consider both weak anisotropy and large anisotropy, and allow the occupancy to be parametrically large or small. Writing the typical momentum of an initial excitation as Q and the final temperature as T final , full equilibration occurs in a time t eq ∼ α −2 T −1 final for T final > Q, and t eq ∼ α −2 Q 1 2 T −3 2 final for T final < Q, unless the initial system is sufficiently anisotropic and T final > α 2 3 Q, in which case equilibration occurs somewhat faster, t eq ∼ max(α −2 T −1 , α −13 7 Q 5 7 T −12 7 final ).

Thermalization of mini-jets in a quark-gluon plasma

“…(3.6) admits the turbulent spectrum f ∝ 1/p 7/2 as a fixed point [28,36,41]. On the other hand, it does not vanish when f approaches the thermal distribution f eq (p) ∝ e −p/T .…”

“…Then the parton cascades produced via successive branchings are themselves dominated by hard gluons, with energies ω T , whose emissions are controlled by the BDMPSZ mechanism 1 [2][3][4][5], that is, by multiple soft scattering in the medium. A distinguished feature of this mechanism is that it favors 'quasi-democratic branchings' [28,36,41], leading to a phenomenon of wave turbulence [28]: via successive splittings, the energy flows from one parton generation to the next one, without accumulating at any intermediate step (see section 2 below for details).…”

“…for a gluon with energy ω to undergo a 'quasi-democratic' branching [28,36,41]. This duration t br (ω) should be compared to the medium size L which is available to that parton:…”

Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution

“…This part of the evolution is characterized by negative values of the longitudinal pressure P L , which is a result of the coherence of the approximately boost invariant fields. However, classical numerical simulations [21,29] (as well as analytical series solutions to the classical equations of motion [30,31]) show that in a timescale Q s τ ∼ 1, the coherence is lost, the longitudinal pressure approaches zero P L ∼ 0, and the occupancies become perturbative [32][33][34][35]. At this point the system may be passed to the EKT [16,[36][37][38].…”

Symmetric and asymmetric reheating

“…Even in perturbative reheating scenarios, the dynamics can be modified significantly by thermal and plasma effects [77,[79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94]. Thermal masses produced as a sector heats up could modify or block energy transport [81], and energy transfer by scattering can be important, as can the quasiparticle and collective excitation dynamics [77].…”