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 , which is dual to a d−dimensional conformal field theory (CFT) in hyperbolic space with temperature T = 1/(2π ). We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity v B (T ) nicely interpolates between the Rindler-AdS result v B (T = 1 2π ) = 1 d−1 and the planar result v B (T 1 ) = d 2(d−1) .arXiv:1907.08030v2 [hep-th]

Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in d-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.

As a means to support the access of massive machine-type communication devices, grant-free access and non-orthogonal multiple access (NOMA) have received great deal of attention in recent years. In the grant-free transmission, each device transmits information without the granting process so that the basestation needs to identify the active devices among all potential devices. This process, called an active user detection (AUD), is a challenging problem in the NOMA-based systems since it is difficult to identify active devices from the superimposed received signal. An aim of this paper is to put forth a new type of AUD based on deep neural network (DNN). By applying the training data in the properly designed DNN, the proposed AUD scheme learns the nonlinear mapping between the received NOMA signal and indices of active devices. As a result, the trained DNN can handle the whole AUD process, achieving an accurate detection of the active users. Numerical results demonstrate that the proposed AUD scheme outperforms the conventional approaches in both AUD success probability and computational complexity.By exploiting the fact that only a few active devices in a cell transmit the information concurrently (see Fig. 1), the AUD problem can be readily formulated as a sparse recovery problem [8], [9]. Since the transmit vector is sparse, compressed sensing (CS) technique has been popularly employed [10], [11]. In [8], the AUD problem is modeled as a single measurement vector (SMV) problem and MPA is used to solve the problem. In this CS-based AUD scheme, basestation detects devices based on the correlation between the received signal and device specific sequence. However, performance of the CS-based AUD is not that appealing when the columns of a system matrix (a.k.a. sensing matrix) are highly correlated and sparsity (the number of nonzero elements) of the underlying input vector increases. In fact, in the practical NOMAbased transmission, correlation among the NOMA sequences and also device activity (sparsity) are relatively high so that the CS-based AUD might not be effective. Indeed, it has been shown that the performance of the sparse recovery algorithm is degraded significantly when the mutual correlation and sparsity increase [11]. Therefore, it is of importance to come up with a new type of AUD scheme suitable for the overloaded yet less sparse access scenarios.An aim of this paper is to pursue an entirely different approach to detect active users in the grant-free NOMA scenario. For an efficient and accurate AUD, we exploit the deep neural network (DNN), a learning-based tool to approximate the complicated and nonlinear function.Over the years, DNN has been successfully applied in numerous applications such as image classification [12], machine translation [13], automatic speech recognition [14], and Go game [15].Recently, DNN has been also applied to various wireless systems such as multiple-input and multiple-output (MIMO) detection, wireless scheduling, and direction-of-arrival (DoA) estimation [16]. In these w...

We study a relation between the thermal diffusivity (D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity (v B ) in strongly correlated systems by using a holographic method. Recently, it was shown thatis universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for E i in terms of the critical dynamical exponents z i in each direction, E i = z i /2(z i − 1). Furthermore, we find the lower bound of E i is always 1/2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy.