Weak Field Collapse in AdS: Introducing a Charge Density
  We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large $N_c$ gauge theory in $(2+1)$-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis. 
Elena Caceres, Arnab Kundu, Juan F. Pedraza and Di-Lun Yang
hep-th cond-mat.str-el gr-qc nucl-th