# Viscoelastic Dynamics in Holography

## TL;DR

This paper investigates the viscoelastic response in holographic models, revealing that the traditional Maxwell relaxation time often misestimates the actual relaxation time, especially at low temperatures, and exhibits overshoot phenomena.

## Contribution

It provides explicit calculations of relaxation times in holographic models, showing deviations from the Maxwell relaxation time and analyzing temperature-dependent behaviors.

## Key findings

- At high temperatures, $ au_M$ slightly overestimates the actual relaxation time.
- At low temperatures, $ au_M$ underestimates the relaxation time significantly.
- The real-time response can show overshoot phenomena before relaxation.

## 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 $\tau_M$, which has been identified traditionally with the relaxation time scale. We compute explicitly the relaxation time in our examples and that it differs from $\tau_M$. At high temperatures $\tau_M$ 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: $\tau_M$ underestimates the actual relaxation time, in some cases quite drastically. Moreover, when $\tau_M$ 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.