Quantum quenches of holographic plasmas

TL;DR

This paper uses holography to study finite-temperature quantum quenches in a four-dimensional CFT, where the boundary coupling to a relevant operator of dimension $2<\Delta<4$ is turned on with a fixed timescale. By analyzing linearized bulk scalar dynamics around an AdS$_5$ black hole and performing holographic renormalization, the authors compute $\langle\mathcal{O}_\Delta\rangle$ and $\langle T_{\mu\nu}\rangle$ during the quench and extract the final thermodynamic state. They demonstrate universal scaling in fast quenches, with observables scaling as powers of $\alpha$ determined by $\Delta$, and show the relaxation time is governed by the thermal timescale $1/T$ regardless of $\Delta$ or quench rate. In slow quenches, the system approaches adiabatic behavior with predictable $1/\alpha$ corrections; entropy production remains nonnegative and aligns with thermodynamic expectations. The results offer a controlled, nonperturbative view of far-from-equilibrium dynamics in strongly coupled plasmas and highlight universal features of holographic quantum quenches.

Abstract

We employ holographic techniques to study quantum quenches at finite temperature, where the quenches involve varying the coupling of the boundary theory to a relevant operator with an arbitrary conformal dimension $2\leq\D\leq4$. The evolution of the system is studied by evaluating the expectation value of the quenched operator and the stress tensor throughout the process. The time dependence of the new coupling is characterized by a fixed timescale and the response of the observables depends on the ratio of the this timescale to the initial temperature. The observables exhibit universal scaling behaviours when the transitions are either fast or slow, i.e. when this ratio is very small or very large. The scaling exponents are smooth functions of the operator dimension. We find that in fast quenches, the relaxation time is set by the thermal timescale regardless of the operator dimension or the precise quenching rate.

Figures (10)

• Figure 1: (Colour online) Plots of the response coefficient $\phi_{(2\Delta-4)}$ for quenches of different speeds, in the fast quench regime. Time is rescaled by a factor of $1/\alpha$ and the value of $\phi_{(2\Delta-4)}$ is rescaled by $\alpha^{2\Delta-4}$. Clockwise from the top left, the plots are for $\Delta=7/3$, $8/3$, $11/3$ and $10/3$. In each case, the response is presented for $\alpha=1$ (dashed), $1/2$(brown), $1/4$ (blue), $1/8$ (purple), $1/16$ (green), $1/32$ (orange) and $1/64$ (red) (as well as $\alpha=1/128$ (yellow) for $\Delta=7/3$).
• Figure 2: (Colour online) Plots of $\phi_{(2\Delta-4)}$ for quenches of different speeds, in the fast quench regime. $\phi_{(2\Delta-4)}$ is rescaled by $\alpha^{2\Delta-4}$ and is plotted against the actual value of the source $\phi_{(0)}$. Clockwise from the top left, the plots are for $\Delta=7/3$, $8/3$, $11/3$ and $10/3$. In each case, the response is presented for various values of $\alpha$, which are indicated using the same colour scheme as in figure \ref{['p12fast']}.
• Figure 3: $\log$-$\log$ plots for $-a_{2,4}(\infty)$ versus $\alpha$ for various $\Delta$, in the fast quench regime. The straight lines shown are least-squares fits through the three leftmost data-points in each case. The fact that the plots tend to straight lines for negative values of $\log\alpha$ means that $a_{2,4}(\infty)$ scales as a power law for small $\alpha$. Clockwise from the top left, the plots are for $\Delta=7/3$, $8/3$, $11/3$ and $10/3$.
• Figure 4: (Colour online) Plot of the asymptotic scaling of $-a_{2,4}(\infty)$ as a power of $\alpha$, in the fast quench limit. The line shown is the predicted theoretical trend $\frac{-d\log(-a_{2,4}(\infty))}{d\log\alpha}=2\Delta-4$. Points shown are for $\Delta=2$, $7/3$, $8/3$, $3$, $10/3$, $11/3$ and $4$. The datapoints for $\Delta=2,3$ are taken from blm. The datapoint for $\Delta=4$ is taken from blmn.
• Figure 5: (Colour online) Plots of $\phi_{(2\Delta-4)}$ for quenches of different speeds in the slow quench regime. Time is rescaled by a factor of $\alpha^{-1}$ and the value of $\phi_{(2\Delta-4)}$ is rescaled by $\alpha^{2\Delta-4}$. Plots for larger $\alpha$ follow an inverted $\tanh$-profile more closely, which is a negative constant times the source. Clockwise from the top left, the plots are for $\Delta=7/3$, $8/3$, $11/3$ and $10/3$. In each case, the response is presented for $\alpha=1$ (dashed), $2$ (brown), $4$ (blue), $8$ (purple), $16$ (green), $32$ (orange) and $64$ (red).