Holographic Thermalization with Chemical Potential

TL;DR

This paper investigates how chemical potential influences the thermalization process in strongly coupled quantum field theories using holographic methods, revealing non-monotonic behavior in thermalization times related to probe size and chemical potential.

Contribution

It introduces a holographic analysis of thermalization with chemical potential, highlighting the non-monotonic dependence of thermalization time on chemical potential and probe size.

Findings

Entanglement entropy thermalizes last, setting the equilibration timescale.

Thermalization time exhibits non-monotonic dependence on chemical potential for small probe sizes.

Different regimes of thermalization behavior are identified based on probe size and 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-Nordstr\"om 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.