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In a quantum field theory, apparent thermalization can be a consequence of entanglement as opposed to scatterings. We discuss here how this can help to explain open puzzles such as the success of thermal models in electron-positron collisions. It turns out that an expanding relativistic string described by the Schwinger model (which also underlies the Lund model) has at early times an entanglement entropy that is extensive in rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_tau=hbar/(2pi k_Btau)$, even in the absence of any scatterings.
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Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a quench, via calculations of two-point functions, Wilson loops and entanglement entropy in d=2,3,4. In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects - geodesics, minimal surfaces and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.
We develop a holographic model for thermalization following a quench near a quantum critical point with non-trivial dynamical critical exponent. The anti-de Sitter Vaidya null collapse geometry is generalized to asymptotically Lifshitz spacetime. Non-local observables such as two-point functions and entanglement entropy in this background then provide information about the length and time scales relevant to thermalization. The propagation of thermalization exhibits similar horizon behavior as has been seen previously in the conformal case and we give a heuristic argument for why it also appears here. Finally, analytic upper bounds are obtained for the thermalization rates of the non-local observables.
The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated over the Vaidya-AdS geometry. We numerically determine the Hubeny-Rangamani-Takayanagi (HRT) surface which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of two radii, it undergoes a phase transition or double phase transitions from a hemi-torus configuration to a two-disk configuration, or vice versa, during the thermalization. The occurrence of various phase transitions is determined by the ratio of two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with double phase transitions. Finally, if the quench process is fairly slow which may be controlled by the thickness of null shell, the region with double phase transitions vanishes.
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 set of non-linear Einstein equations supplemented with specific time dependent boundary conditions. The resulting solutions allow one to comment on the timescale by which the perturbed states thermalize, as well as to quantify the properties of the final state as a function of the perturbation parameters. We comment on the influence of the dual gauge theorys confinement scale on these results, as well as the appearance of a previously anticipated universal scaling regime in the abrupt quench limit.
We study glueballs in the holographic gauge theories living in a curved space-time. The dual bulk is obtained as a solution of the type IIB superstring theory with two parameters, which correspond to four dimensional (4D) cosmological constant $lambda$ and the dark radiation $C$ respectively. The theory is in the confining phase for $lambda <0$ and small $C$, then we observe stable glueball states in this theory. However, the stability of the glueball states is lost when the density of the dark radiation ($C$) increases and exceeds a critical point. Above this point, the dark radiation works as the heat bath of the Yang-Mills theory since the event horizon appears. Thus the system is thermalized, and the theory is in a finite temperature deconfinement phase, namely in the QGP phase. We observe this transition process through the glueball spectra which varies dramatically with $C$. We also examined the entanglement entropy of the system to find a clue of this phase transition and the role of the dark radiation $C$ in the entanglement entropy.
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