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 AdSd+1 and AdSd+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 T l and small values of \mu/T the thermalization time decreases as we increase \mu/T, thus the plasma thermalizes faster. For large values of \mu/T the dependence changes and the thermalization time increases with increasing \mu/T . On the other hand, if we increase the value of T l 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 T l << 1 and monotonic for T l >> 1.

Comments: 49 pages, v2 references added, typo corrected