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.
Highlights
The difference between a rigid solid and a flowing liquid appears to be very neat and clear in our everyday experience
In the remainder of this paper we shall study the viscoelastic properties of the massive gravity models of [9,18] by computing the complex modulus and the response under time dependent sources
Once GðωÞ is obtained we can compute the real-time response of a system under an external and time dependent source σðtÞ
Summary
The difference between a rigid solid and a flowing liquid appears to be very neat and clear in our everyday experience. Progress has been made to introduce elastic effects due to the spontaneous breaking of translational invariance and coexisting with the viscous properties implied by the presence of a black hole horizon, i.e., finite temperature In this direction, a promising direction to describe viscoelastic materials within holography is given by “massive gravity” theories [9,10].1. In the remainder of this paper we shall study the viscoelastic properties of the massive gravity models of [9,18] by computing the complex modulus and the response under time dependent sources This opens the possibility of studying viscoelastic effects in strongly coupled materials or systems at quantum criticality. IV we summarize our findings and propose some future directions
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