Holographic approach of the spinodal instability to criticality

Abstract

A smoking gun signature for a first-order phase transition with negative speed of sound squared $$ {c}_s^2 $$ c s 2 is the occurrence of a spinodal instability. In the gauge/gravity duality it corresponds to a Gregory-Laflamme type instability, which can be numerically simulated as the evolution of unstable planar black branes. Making use of holography its dynamics is studied far from and near a critical point with the following results. Near a critical point the interface between cold and hot stable phases, given by its width and surface tension, is found to feature a wider phase separation and a smaller surface tension. Far away from a critical point the formation time of the spinodal instability is reduced. Across softer and harder phase transitions, it is demonstrated that mergers of equilibrated peaks and unstable plateaux lead to the preferred final single phase separated solution. Finally, a new atypical setup with dissipation of a peak into a plateau is discovered. In order to distinguish the inhomogeneous states I propose a new criterium based on the maximum of the transverse pressure at the interface which encodes phase-mixed peaks versus fully phase separated plateaux.

A simple description of holographic domain walls in confining theories — extended hydrodynamics

“…We believe, however, that the resulting framework should have a much more general range of applicability. Indeed quite different (nonconformal) holographic models, which have a 1 st order phase transition between two deconfined phases exhibit a domain wall profile which is very well fitted by a tanh function [7,9]. Since an underlying tanh shape of the domain wall arises analytically in our framework, this suggests that the framework could also be applied in those settings.…”

“…From the action (5.18), we derive equations of motion for γ as well as the energy-momentum tensor, whose conservation laws yield the remaining equations of motion for the hydrodynamic degrees of freedom. 9 In order to fully specify the above action, we need to pick the prefactor a(γ) and the potential V (γ). Furthermore, we need to express Γ(γ) in terms of the elementary scalar field γ.…”

“…In the early years of the AdS/CFT correspondence, phase transitions were primarily studied in the equilibrium setting by comparing the free energies of two distinct dual gravitational backgrounds. The issue of describing a passage through the phase transition in real time has only been addressed quite recently in a number of works, starting from a linearized analysis [1,2] to fully dynamical studies of phase separation and domain wall dynamics [3][4][5][6][7][8][9][10].…”

Holographic approach of the spinodal instability to criticality

“…Therefore this untypical dissipation process does not depend on criticality. In the number of simulations [57,60] performed up to date this process has not yet been observed in large extents, where several peaks or plateaux initially form. While peaks with a slow velocity form on a regular basis it is quite untypical for the spinodal instability to morph into quasi-static features.…”

“…This is much faster than numerical noise which needs to build up the unstable modes from amplitudes below 10 −12 . All the boundary data of the simulations is published for further analysis or comparisons as open data on a Zenodo repository [57]. As all the chosen initial local energy densities are in the dynamical unstable region between E low and E high of each theory, the plasma will be subject to the spinodal instability, whose dynamical properties one is interested in.…”