Holographic thermalization with chemical potential

Abstract

We study the thermalization of a strongly coupled quantum field theory in the presence of a chemical potential. More precisely, using the holographic prescription, we calculate non-local operators such as two point function, Wilson loop and entanglement entropy in a time-dependent background that interpolates between AdS d+1 and AdS d+1-Reissner-Nordström for d = 3, 4. We find that it is the entanglement entropy that thermalizes the latest and thus sets a time-scale for equilibration in the field theory. We study the dependence of the thermalization time on the probe length and the chemical potential. We find an interesting non-monotonic behavior. For a fixed small value of Tℓ and small values of μ/T the thermalization time decreases as we increase μ/T, thus the plasma thermalizes faster. For large values of μ/T the dependence changes and the thermalization time increases with increasing μ/T. On the other hand, if we increase the value of (Tℓ) this non-monotonic behavior becomes less pronounced and eventually disappears indicating two different regimes for the physics of thermalization: non-monotonic dependence of the thermalization time on the chemical potential for Tℓ ≪ 1 and monotonic for Tℓ ≫ 1.