Strongly and Weakly Unstable Anisotropic Quark-Gluon Plasma

Abstract

Using explicit solutions of the QCD transport equations, we construct an effective potential for an anisotropic quark-gluon plasma which under plausible assumptions holds beyond the Hard Loop approximation. The configurations, which are unstable in the linear response approach, are characterized by a negative quadratic term of the effective potential. The signs of higher order terms can be either negative or positive, depending on the parton momentum distribution. In the case of a Gaussian momentum distribution, the potential is negative and unbound from below. Therefore, the modes, which are unstable for gauge fields of small amplitude, remain unstable for arbitrary large amplitudes. We also present an example of a momentum distribution which gives a negative quadratic term of the effective potential but the whole potential has a minimum and it grows for sufficiently large gauge fields. Then, the system is weakly unstable. The character of the instability is important for the dynamical evolution of the plasma system.

13 pages, 1 figure, revised, to appear in Phys. Rev. D

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• Isotropization by QCD Plasma Instabilities
• Deconfinement transition dynamics and early thermalization in QGP
• Thermalization vs. Isotropization & Azimuthal Fluctuations
• Three-body force effect on the properties of nuclear matter under the gap and continuous choices within the BHF approach