Dynamics of phase separation from holography

Abstract

We use holography to develop a physical picture of the real-time evolution of the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a firstorder, thermal phase transition. We numerically solve Einstein's equations to follow the evolution, in which we identify four generic stages: A first, linear stage in which the instability grows exponentially; a second, non-linear stage in which peaks and/or phase domains are formed; a third stage in which these structures merge; and a fourth stage in which the system finally relaxes to a static, phase-separated configuration. On the gravity side the latter is described by a static, stable, inhomogeneous horizon. We conjecture and provide evidence that all static, non-phase separated configurations in large enough boxes are dynamically unstable. We show that all four stages are well described by the constitutive relations of second-order hydrodynamics that include all second-order gradients that are purely spatial in the local rest frame. In contrast, a Müller-Israel-Stewart-type formulation of hydrodynamics fails to provide a good description for two reasons. First, it misses some large, purely-spatial gradient corrections. Second, several second-order transport coefficients in this formulation, including the relaxation times τ π and τ Π , diverge at the points where the speed of sound vanishes.

Crossing a large-N phase transition at finite volume

“…If the system of interest is an interacting, four-dimensional quantum field theory then following the real-time evolution from an unstable homogeneous state to a phase-separated configuration can be extremely challenging with conventional methods. For this reason, in [1,2] holography was used to study this evolution in the case of a four-dimensional gauge theory with a gravity dual (see also [3,4] for a case in which the gauge theory is three-dimensional). In order to regularise the problem, refs.…”

“…In order to regularise the problem, refs. [1,2] considered the gauge theory formulated on R 1,2 × S 1 with periodic boundary conditions on a circle of size L. For simplicity, translational invariance along the non-compact spatial directions was imposed, thus effectively reducing the dynamics to a 1+1 dimensional problem along time and the compact direction. The compactness of the circle makes the spectrum of perturbations discrete and simplifies the technical treatment of the problem.…”

“…[1] provided a first example of the time evolution from a homogeneous state to an inhomogeneous one. A systematic study was then performed in [2]. In this reference the focus was on the infinitevolume limit, understood as the limit in which L is much larger than any other scale in the problem such as the microscopic gauge theory scale Λ, the size of the interface, etc.…”

Holographic boiling and generalized thermodynamic description beyond local equilibrium

“…In a recent paper [26], the authors realized a dynamic process of domain wall formation holographically. There are also some other progresses in this topic [27,28]. However, in these studies the holographic systems are effectively 1D, so more realistic structures like bubbles (at least 2D) cannot be considered.…”

Dynamics near a first order phase transition

“…Apart from the locations of the domain walls 3. Similar physics is very relevant in 3+1 dimensions in a cosmological context, see e.g [22,14]…”