The space of transport coefficients allowed by causality.

As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we adopt a more general approach, deploying bootstrap techniques to rule out theories that are inconsistent with microscopic causality.

Prescaling Relaxation to Nonthermal Attractors.

We study how isotropic and homogeneous far-from-equilibrium quantum systems relax to nonthermal attractors, which are of interest for cold atoms and nuclear collisions. We demonstrate that a first-order ordinary differential equation governs the self-similar approach to nonthermal attractors, i.e.

Rigorous Bounds on Transport from Causality.

We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal dissipative dispersion relations have a finite radius of convergence in cases where stochastic fluctuations are negligible. We then give two-sided bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.

Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium.

We study the dynamics of perturbations around nonthermal fixed points associated with universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions, we determine the stability scaling exponents using a self-consistent large-N expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasiexponential deviations from the fixed point in the infrared.

Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow.

The gradient expansion is the fundamental organizing principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to address this question in a class of fluids modeled by Israel-Stewart-type relaxation equations. We apply it to (1+1)-dimensional flows and provide numerical evidence for factorially divergent gradient expansions.

Long Distance Entanglement of Purification and Reflected Entropy in Conformal Field Theory.

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both the entanglement of purification and reflected entropy is enhanced with respect to the mutual information behavior by a logarithm of the distance between the subregions.

Conformal field theory complexity from Euler-Arnold equations.

Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest.

Hydrodynamic Attractors in Phase Space.

Hydrodynamic attractors have recently gained prominence in the context of early stages of ultrarelativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions.

Path Integral Optimization as Circuit Complexity.

Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations of the Euclidean path integral that prepare a given operator or state may provide an alternative definition, whose connection to the standard notion of complexity is less apparent. In this Letter, we bridge the gap between these two proposals in two-dimensional conformal field theories, by explicitly showing how the latter approach from path integral optimization may be given by a concrete realization within the standard gate counting framework.

Complexity as a Novel Probe of Quantum Quenches: Universal Scalings and Purifications.

We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits universal scalings in both the slow and fast quench regimes. We then generalize our results to a one-dimensional harmonic chain, and show that preservation of these scaling behaviors in free field theory depends on the choice of norm.

Toward a Definition of Complexity for Quantum Field Theory States.

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric.

New theories of relativistic hydrodynamics in the LHC era.

The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our review presents these developments from the perspective of the underlying microscopic physics, using the language of quantum field theory, relativistic kinetic theory, and holography. We discuss the gradient expansion, the phenomenon of hydrodynamization, as well as several models of hydrodynamic evolution equations, highlighting the interplay between collective long-lived and transient modes in relativistic matter.

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory.

We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere.

Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation.

Consistent formulations of relativistic viscous hydrodynamics involve short-lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Müller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation.

Equilibration Rates in a Strongly Coupled Nonconformal Quark-Gluon Plasma.

We initiate the study of equilibration rates of strongly coupled quark-gluon plasmas in the absence of conformal symmetry. We primarily consider a supersymmetric mass deformation within N=2^{*} gauge theory and use holography to compute quasinormal modes of a variety of scalar operators, as well as the energy-momentum tensor. In each case, the lowest quasinormal frequency, which provides an approximate upper bound on the thermalization time, is proportional to temperature, up to a prefactor with only a mild temperature dependence.

Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma.

Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal role in our understanding of heavy ion collisions at RHIC and LHC. They are based on a phenomenological description due to Müller, Israel, Stewart (MIS) and others, which incorporates viscous effects and ensures a well-posed initial value problem. Focusing on the case of conformal plasma we propose a generalization which includes, in addition, the dynamics of the least damped far-from-equilibrium degree of freedom found in strongly coupled plasmas through the AdS/CFT correspondence.

Longitudinal coherence in a holographic model of asymmetric collisions.

As a model of the longitudinal structure in heavy ion collisions, we simulate gravitational shock wave collisions in anti-de Sitter space in which each shock is composed of multiple constituents. We find that all constituents act coherently, and their separation leaves no imprint on the resulting plasma, when this separation is ≲0.26/T_{hyd}, with T_{hyd} the temperature of the plasma at the time when hydrodynamics first becomes applicable.

From full stopping to transparency in a holographic model of heavy ion collisions.

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model.

Hydrodynamic gradient expansion in gauge theory plasmas.

We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives.

Characteristics of thermalization of boost-invariant plasma from holography.

We report on the approach toward the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at τ=0. The results are obtained through a numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article [M. P.

Strong coupling isotropization of non-abelian plasmas simplified.

We study the isotropization of a homogeneous, strongly coupled, non-abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full nonlinear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies.

Consistent holographic description of boost-invariant plasma.

Prior attempts to construct the gravity dual of boost-invariant flow of N=4 supersymmetric Yang-Mills gauge theory plasma suffered from apparent curvature singularities in the late-time expansion. This Letter shows how these problems can be resolved by a different choice of expansion parameter. The calculations presented correctly reproduce the plasma energy-momentum tensor within the framework of second-order viscous hydrodynamics.

A small RNA in testis and brain: implications for male germ cell development.

BC1 RNA, a small non-coding RNA polymerase III transcript, is selectively targeted to dendritic domains of a subset of neurons in the rodent nervous system. It has been implicated in the regulation of local protein synthesis in postsynaptic microdomains. The gene encoding BC1 RNA has been suggested to be a master gene for repetitive ID elements that are found interspersed throughout rodent genomes.