Viscoelastic Dynamics in Holography

Abstract

We study the mechanical response under time-dependent sources of a simple class of holographic models that exhibit viscoelastic features. The ratio of viscosity over elastic modulus defines an intrinsic relaxation time scale -- the so-called Maxwell relaxation time $\ddot{I}{„}_M$, which has been identified traditionally with the relaxation time scale. We compute explicitly the relaxation time in our examples and that it differs from $\ddot{I}{„}_M$. At high temperatures $\ddot{I}{„}_M$ over-estimates the actual relaxation time, although not by much and moreover it still captures reasonably well the temperature behaviour. At sufficiently low temperatures the situation is reversed: $\ddot{I}{„}_M$ underestimates the actual relaxation time, in some cases quite drastically. Moreover, when $\ddot{I}{„}_M$ under-estimates the real-time response exhibits an overshoot phenomenon before relaxation. We comment on the $T=0$ limit, where the relaxation is power-law because our models exhibit criticality.

matching the published version in PRD