We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.

We give a holographic description of global conformal blocks in two dimensional conformal field theory on the sphere and on the torus. We show that the conformal blocks for one-point functions on the torus can be written as Witten diagrams in thermal AdS. This is accomplished by deriving a general conformal Casimir equation for global conformal blocks, and showing that Witten diagrams obey the same equation. We study the semiclassical limit of n-point conformal blocks, and show that these equal the action of a network of bulk world-lines obeying appropriate geodesic equations. We give an alternate description in the Chern-Simons formulation of 3D gravity, where the conformal blocks are described by networks of Wilson lines, and argue that these formulations are equivalent.

The eikonal phase which determines the Regge limit of the gravitational scattering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been computed to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single stress tensor conformal block, but the subleading term is a result of an infinite sum of the double stress tensor contributions. We provide a closed form expression for the OPE coefficients of the leading twist double stress tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.

The asymptotic symmetry group (ASG) at future null infinity (I + ) of four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I + . Finite charges are constructed for each choice of ASG generator together with a two-surface on I + . A conservation equation is derived relating the evolution of the charges with the radiation flux through I + .arXiv:1009.4730v1 [gr-qc]

One of the most fascinating experimental achievements of the last decade was the realization of Bose-Einstein Condensation (BEC) of ultra-cold atoms in optical lattices (OL's) [1,2,3,4]. The extraordinary level of control over these structures allows us to investigate complex solid state phenomena [4,5,6,7,8,9] and the emerging eld of atomtronics promises a new generation of nanoscale devices. It is therefore of fundamental and technological importance to understand their dynamical properties. Here we study the outgoing atomic ux of BECs loaded in a one dimensional OL with leaking edges, using a mean eld description provided by the Discrete Non-Linear Schrodinger Equation (DNLSE). We demonstrate that the atom population inside the OL decays in avalanches of size J. For intermediate values of the interatomic interaction strength their distribution P (J) follows a power law i.e. P(J) ∼ 1/J α characterizing systems at phase transition. This scale free behaviour of P(J) reects the complexity and the hierarchical structure of the underlying classical mixed phase space. Our results are relevant in a variety of contexts (whenever DNLSE is adequate), most prominently the light emmitance from coupled non-linear optics waveguides [12].An optical lattice with a controlled leakage of the atomic BEC can be realized experimentally by the action of two separate continous microwave or Raman lasers to locally spin-ip BEC atoms (at the edges of the OL) to a nontrapped state [10,11]. The spin-ipped atoms do not experience the magnetic trapping potential and are released through gravity in two atomic beams at the ends of the OL. The mathematical model (see Method section) that describes the dynamics of the BEC in a leaking OL of size M iswhere γ describes the atomic losses and N n = |ψ n | 2 is the atomic population at site n. Below we study the decay (due to leakage) of the total atom population N (τ ) = n N n (τ ) inside the OL as a function of the initial eective interaction strength i.e. Λ = χN (τ = 0)/M . An exciting result appearing in the frame of nonlinear lattices is the existence of stationary, spatially localized solutions, termed Discrete Breathers (DB), which emerge due to the nonlinearity and discreteness of the system. DBs were observed in various experimental setups [15,16,17,18,19,20] while their existence and stability were studied thoroughly during the last decade [21,22,23,24,25]. Their importance was already recognized in [26] where it was shown that they act as virtual bottlenecks which slow down the relaxation processes in generic nonlinear lattices [25,26,27]. Further works [27] established the fact that absorbing boundaries take generic initial conditions towards self-trapped DB's. Recently the same scenario was proposed for a BEC in a leaking OL where it was observed [10] that N (τ ) decays in sudden bursts J (see inset of Fig. 1). Here, for the rst time we present a full theoretical study of the decay process of N (τ ) and analyze the distribution P(J). We nd three types of dynamical behaviour [14]: For ve...