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 timescale—the so-called Maxwell relaxation time ${\tau }_M$, which has been identified traditionally with the relaxation timescale. We compute explicitly the relaxation time in our examples and find that it differs from ${\tau }_M$. At high temperatures ${\tau }_M$ overestimates the actual relaxation time, although not by much and moreover it still captures reasonably well the temperature behavior. At sufficiently low temperatures the situation is reversed: ${\tau }_M$ underestimates the actual relaxation time, in some cases quite drastically. Moreover, when ${\tau }_M$ underestimates 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.

• Received 10 October 2019

DOI:https://doi.org/10.1103/PhysRevD.100.106014

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society