We identify the universal mechanism behind the thermalization of (1+1)d QFTs at high and low temperatures. Viewing these theories as CFTs perturbed by relevant or irrelevant deformations, we show that conformal perturbation theory in the thermal state breaks down at late times allowing for the emergence of hydrodynamics. This breakdown occurs universally due to the unsuppressed exchange of stress tensors near the lightcone. Furthermore, for theories with central charge $c\rightarrow\infty$ we solve for the emergent hydrodynamic theory to all orders in the gradient expansion by arguing that all transport parameters appearing in two-point functions have universal expressions in terms of the scaling dimension $Δ$ of the perturbation. The radius of convergence of the hydrodynamic dispersion relations provides an early time cutoff for hydrodynamics, which agrees with the time scale at which conformal perturbation theory breaks down.
We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than $\frac{1}{T}$, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic $C$-function, and constrain the sign of the $\mathcal T\bar{\mathcal T}$ term in EFTs.
In this paper, based on the fundamental principles of Gauge/gravity duality and considering a \textit{global quench}, we probe the physics of thermalization for a special class of strongly coupled non relativistic QFTs by computing the entanglement entropy of the plasma. The isometry group of such QFTs is comprised of the generators of the Schrödinger algebra which could be precisely realized as an isometry group of the killing generators of an asymptotically Schrödinger $ Dp $ brane space time. In our analysis, we note that during the pre local stages of the thermal equilibrium the entangleme…
In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situ…
We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibriu…
We consider the time evolution of entanglement entropy after a global quench in a strongly coupled holographic system, whose subsequent equilibration is described in the gravity dual by the gravitational collapse of a thin shell of matter resulting in a black hole. In the limit of large regions of entanglement, the evolution of entanglement entropy is controlled by the geometry around and inside the event horizon of the black hole, resulting in regimes of pre-local- equilibration quadratic growth (in time), post-local-equilibration linear growth, a late-time regime in which the evolution does …
In gauge/gravity duality framework the thermalization of mesons in strongly coupled (p+1)-dimensional gauge theories is studied for a general Dp-Dq system, q>=p, using the flavour Dq-brane as a probe. Thermalization corresponds to the horizon formation on the flavour Dq-brane. We calculate the thermalization time-scale due to a time-dependent change in the baryon number chemical potential, baryon injection in the field theory. We observe that for such a general system it has a universal behaviour depending only on the t'Hooft coupling constant and the two parameters which describe how we injec…
QFTs with local topological operators feature unusual sectors called "universes," which are separated by infinite-tension domain walls. We show that such systems have relevant deformations with exactly-calculable effects. These deformations allow one to dial the vacuum energy densities of the universes. We describe applications of these deformations to confinement in 2d gauge theories, as well as a curious violation of the effective field theory naturalness principle.
The universal nature of black hole collapse in asymptotically $AdS_3$ gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge $c$. It is known that non-equilibrium states with scaling dimensions of order $c$ can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's equation it is shown that a state that fails to thermalize can be promoted to a …
We study thermalization of strongly coupled gauge theory plasma in the presence of magnetic field using the AdS/CFT correspondence. We utilize the falling energy-shell model as a holographic description of gauge theory plasma undergoing thermalization, and find the effect of magnetic field on thermalization time in various space-time dimensions. Our results demonstrate that magnetic field universally hastens thermalization of strongly coupled gauge theory plasma.
We study the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. We find that the Hartree approximation is remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by numerically solving the equations of motion in light-cone coor…
Using the AdS/CFT correspondence for strongly coupled gauge theories, we calculate thermalization of mesons caused by a time-dependent change of a baryon number chemical potential. On the gravity side, the thermalization corresponds to a horizon formation on the probe flavor brane in the AdS throat. Since heavy ion collisions are locally approximated by a sudden change of the baryon number chemical potential, we discuss implication of our results to RHIC and LHC experiments, to find a rough estimate of rather rapid thermalization time-scale t_{th} < 1 [fm/c]. We also discuss universality of ou…
Hydrodynamics is a universal effective theory describing relaxation of quantum field theories towards equilibrium. Massive QFTs in de Sitter spacetime are never at equilibrium. We use holographic gauge theory/gravity correspondence to describe relaxation of a QFT to its Bunch-Davies vacuum - an attractor of its late-time dynamics. Specifically, we compute the analogue of the quasinormal modes describing the relaxation of a holographic toy model QFT in de Sitter.
The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators -- which are generically expected to create thermal states -- can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients $C_{HH'L}$, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away …
In the framework of AdS$_3$/ CFT$_2$ correspondence, we present a systematic analysis of the late time thermalization of a two dimensional CFT state created by insertion of small number of heavy operators on the vacuum. We show that at late Lorentzian time, the universal features of this thermalization are solely captured by the eigenvalues of the monodromy matrix corresponding to the solutions of the uniformization equation. We discuss two different ways to extract the monodromy eigenvalues while bypassing the need for finding explicitly the full monodromy matrix - first, using a monodromy pr…
We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. The quenches are such that a spatially uniform density of energy is injected at an instant in time, exciting a strongly coupled CFT which eventually equilibrates. Such quench processes are described on the gravity side by the gravitational collapse of a thin shell that results in a black hole. Various nonlocal observables have a unified description in terms of the area of extremal surfaces of different dimensions. In the large distance lim…
We study holographic thermalization in spacetimes with a chemical potential and a non-trivial dilaton field. Three non-local observables are used to probe the whole process and investigate the effect of the ratio of the chemical potential over temperature $χ$ and the dilaton-Maxwell coupling constant $α$. It is found that the saturation time is not always a monotonically increasing function of $χ$, the situation depends on $α$. When $0 \leqα\leq 1$, larger $χ$ yields longer saturation time, while for $α>1$, the situation becomes more complex. More interesting, we found that although $α$ indeed…
In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the $ R $-charge diffusion for the boundary theory and find that (unlike the case for the pure $ AdS_{4} $ black bran…
We argue that the infall time to the singularity in the interior of a black hole, is always related to a classical thermalization time. This indicates that singularities are related to the equilibration of infalling objects with the microstates of the black hole, but only in the sense of classical equilibration. When the singularity is reached, the quantum state of the black hole, initially a tensor product of the state of the infalling object and that of the black hole, is not yet a "generic" state in the enlarged Hilbert space, so its complexity is not maximal. We relate these observations t…
We investigate the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium dynamics is studied by numerically solving the equations of motion in a light- cone-like discretization of the model for a broad range of initial conditions and energy densities.A smooth cascade of energy towards the ultraviolet is found to be the basic mechanism of thermalization.After an initial transient stage,at a time scale of several hundreds inverse masses,the squared of the field gradient becomes larger than the nonlinear term and …
We derive the equation for the quasi-normal modes corresponding to the scalar excitation of a black hole moving away in the fifth dimension. This geometry is the AdS/CFT dual of a boost-invariant expanding perfect fluid in N=4 SUSY Yang-Mills theory at large proper-time. On the gauge-theory side, the dominant solution of the equation describes the decay back to equilibrium of a scalar excitation of the perfect fluid. Its characteristic proper-time can be interpreted as a thermalization time of the perfect fluid, which is a universal (and numerically small) constant in units of the unique scale…
Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
Sharif University of Technology（谢里夫理工大学）；Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences（上海数学与交叉学科研究院）；Seoul National University（首尔大学）；Stony Brook University（石溪大学）
We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the fir…
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $β\ll L$. For times $t$ such that $\ell/2<t<(L-\ell)/2$ the reduced density matrix of a subsystem of length $\ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $\cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/β$. However, for minimal models with $c<1$ (more generally, rational CFTs), …
The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta f…
We study thermalization in the holographic (1+1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench …
We study the holographic entanglement entropy in a homogeneous falling shell background, which is dual to the strongly coupled field theory following a global quench. For d=2 conformal field theories, it is known that the entropy has a linear growth regime if the scale of the entangling region is large. In addition, the growth rate approaches a constant when the scale increases. We demonstrate analytically that this behavior is directly related to the part of minimal area surface probing the interior of apparent horizons in the bulk, as well as the mutual information between two disjoint recta…
We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling $g$, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in $g^2 t/r_s$ (while neglecting order $g^4 t/r_s$ effects) where $r_s = 2GM$ is the Schwarzschild radius. We show that for q…
Time dependent perturbations of states in the holographic dual of a 3+1 dimensional confining theory are considered. The perturbations are induced by varying the coupling to the theory's most relevant operator. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of moti…
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；Department of Physics, Duke University（杜克大学物理系）；Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）；Department of Physics, National Taiwan University（台湾大学物理系）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig Maximilian University of Munich（慕尼黑大学物理系与阿诺德·索末菲理论物理中心）；InQubator for Quantum Simulation, Department of Physics, University of Washington（华盛顿大学物理系量子模拟创新中心）
Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order complexity, which is represented by the eigenstate thermalization hypothesis (ETH) stating that individual energy eigenstates are thermal. Here, we propose a higher-order generalization of the ETH, named the $ k $-ETH ($ k=1,2,\dots $), to quantify higher-order complexity of quantum many-body dynamics at the level of individual energy eigenstates, wh…
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The non-equilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in~\cite{Berges:2013eia} along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the non-equilibrium evolution on large time scales both for non-expanding and expanding non-Abelian plasmas. The turbulent attractor for a non-expanding …
We use top-down gauge theory/string theory correspondence to compute relaxation rates in strongly coupled nonconformal gauge theory plasma. We compare models with difference mechanisms of breaking the scale invariance: "hard breaking" (by relevant operators) and "soft breaking" (by marginal operators). We find that the thermalization time of the transverse traceless fluctuations of the stress-energy tensor is rather insensitive to the mechanisms of breaking the scale invariance over a large range of the scale-breaking parameter $δ=\frac 13-c_s^2$. We comment on the relevance of the results to …
Within a holographic model, we calculate the time evolution of 2-point and 1-point correlation functions (of selected operators) within a charged strongly coupled system of many particles. That system is thermalizing from an anisotropic initial charged state far from equilibrium towards equilibrium while subjected to a constant external magnetic field. One main result is that thermalization times for 2-point functions are significantly (approximately three times) larger than those of 1-point functions. Magnetic field and charge amplify this difference, generally increasing thermalization times…
Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which "real world" theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a …
