Related papers: A Tale of Two Butterflies: An Exact Equivalence in…
In this paper, we revisit the equivalence of two holographic computations of the butterfly velocity: the computation with the shock wave solution and the computation with the entanglement wedge reconstruction. We provide an interpretation…
We study butterfly effect in $D$-dimensional gravitational theories containing terms quadratic in Ricci scalar and Ricci tensor. One observes that due to higher order derivatives in the corresponding equations of motion there are two…
The butterfly velocity characterizes the spread of correlations in a quantum system. Recent work has provided a method of calculating the butterfly velocity of a class of boundary operators using holographic duality. Utilizing this and a…
The butterfly velocity was recently proposed as a characteristic velocity of chaos propagation in a local system. Compared to the Lieb-Robinson velocity that bounds the propagation speed of all perturbations, the butterfly velocity, studied…
We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian ${\cal L}=R+ \Lambda+\alpha R_{\mu\nu\sigma\rho}R^{\mu\nu\sigma\rho}+\beta R_{\mu\nu}R^{\mu\nu}+\gamma…
In the first part of the paper we generalize the butterfly velocity formula to anisotropic spacetime. We apply the formula to evaluate the butterfly velocities in M-branes, D-branes and strings backgrounds. We show that the butterfly…
The black hole butterfly effect is a signal of quantum chaos in holographic theories that can be probed in different ways, including out-of-time-order correlators (OTOCs), pole skipping (PS), and entanglement wedge (EW) reconstruction. Each…
We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information…
We propose a connection between the butterfly velocity and the complexity growth rate in the context of thermodynamics of black holes where the cosmological constant is interpreted as thermodynamic pressure. According to the Smarr formula…
The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via…
When the Lyapunov exponent $\lambda_L$ in a quantum chaotic system saturates the bound $\lambda_L\leqslant 2\pi k_BT$, it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect…
In this work, we study quantum chaos in a variety of holographic QCD models at finite temperature and chemical potentials. This includes the 1 R-Charge black hole (1RCBH) model, the 2 R-Charge black hole (2RCBH) model, a potential…
These notes present a comprehensive analysis of shockwave geometries in holographic settings, focusing on $\textrm{T}\overline{\textrm{T}}$-deformed BTZ black holes and their extensions. By constructing deformed metrics and employing…
In this note we remark that the butterfly effect can be used to diagnose the phase transition of superconductivity in a holographic framework. Specifically, we compute the butterfly velocity in a charged black hole background as well as…
The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered…
In this work, we perform a holographic study to estimate the effect of backreaction on the correlation between two subsystems forming the thermofield double (TFD) state. Each of these subsystems is described as a strongly coupled…
We study the butterfly effect by considering shock wave solutions near the horizon of the AdS black brane in some of 3-dimensional Gravity models including; 3D Einstein Gravity, Minimal Massive 3D Gravity, New Massive Gravity, Generalized…
We study the scrambling properties of $(d+1)$-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius $\ell$, which is dual to a…
The butterfly velocity is commonly used to understand information transport properties in quantum dynamical systems and is related to growth of operators. Here we utilise a quantum teleportation based protocol and Riemannian Trust-Region…
We study the butterfly effect of the AdS planar black holes in the framework of Einstein's general relativity. We find that the butterfly velocities can be expressed by a universal formula $v_{\rm B}^2 = TS/(2V_{\rm th} P)$. In doing so, we…