Collective modes of an anisotropic quark-gluon plasma

Abstract

We analyze the collective modes of high-temperature QCD in the case when there is an anisotropy in the momentum-space distribution function for the gluons. We perform a tensor decomposition of the gluon self-energy and solve the dispersion relations for both stable and unstable modes. Results are presented for a class of anisotropic distribution functions which can be obtained by stretching or squeezing an isotropic distribution function along one direction in momentum space. We find that there are three stable modes and either one or two unstable modes depending on whether the distribution function is stretched or squeezed. The presence of unstable modes which have exponential growth can lead to a more rapid thermalization and isotropization of the soft modes in a quark gluon plasma and therefore may play an important role in the dynamical evolution of a quark-gluon plasma.

Thermalization in weakly coupled nonabelian plasmas

“…This is particularly the case if the system is also anisotropic. In this case, there can be plasma instabilities [6][7][8][9][10][11] which may dominate the dynamics in some cases. To our knowledge, there has been no comprehensive study of this case.…”

“…The process is dominated by small momentum exchange, and in this limit the matrix element becomes 8) where q ⊥ is the momentum transfer in the elastic scattering. In vacuum the total crosssection ∼ d 2 q ⊥ |M | 2 is infrared divergent, but this divergence is regulated by including the medium dependent self-energy to the exchange line in the diagram of Fig.…”

“…8 However, interactions can change the actual spectrum from this production rate. In particular, an f (p) ∼ p −3 spectrum rises more steeply than a thermal spectrum.…”

“…A new complication enters when we consider systems which are locally anisotropic. Namely, certain long-wavelength magnetic gauge field excitations are then generically unstable to exponential growth, in a process called the Weibel instability (see [6] for the electromagnetic case and [7][8][9][10] for an overview of the nonabelian case and [21][22][23] for some nonabelian numerical studies). At weak coupling, in many circumstances these fields are expected to grow large enough that they come to dominate much of the dynamics of the system.…”

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

“…The early-time behavior is then described by plasma instabilities, which have been intensively analyzed over the past years [19][20][21][22]. Classical-statistical simulations show that gluons become highly occupied ∼ 1/α s (Q) after a proper time ∼ Q −1 log 2 (α −1 s ) for expanding systems [23][24][25].…”