Dynamical evolution of spinodal decomposition in holographic superfluids

TL;DR

This paper investigates the real-time nonlinear evolution of spinodal decomposition in holographic superfluids, revealing four stages of phase separation and the role of dynamical heterogeneity, using numerical simulations in a simple holographic model.

Contribution

It introduces a holographic model to study nonlinear spinodal decomposition, confirming linear stability analysis and characterizing the dynamical stages of phase separation.

Findings

Identification of four stages in spinodal decomposition.

Confirmation of a critical length scale related to gradient instability.

Correlation between dynamical heterogeneity and local chemical potential variance.

Abstract

We study the nonlinear dynamical evolution of spinodal decomposition in a first-order superfluid phase transition using a simple holographic model in the probe limit. We first confirm the linear stability analysis based on quasinormal modes and verify the existence of a critical length scale related to a gradient instability -- negative speed of sound squared -- of the superfluid sound mode, which is a consequence of a negative thermodynamic charge susceptibility. We present a comparison between our case and the standard Cahn-Hilliard equation for spinodal instability, in which a critical length scale can be also derived based on a diffusive instability. We then perform several numerical tests which include the nonlinear time evolution directly from an unstable state and fast quenches from a stable to an unstable state in the spinodal region. Our numerical results provide a real time description of spinodal decomposition and phase separation in one and two spatial dimensions. We reveal the existence of four different stages in the dynamical evolution, and characterize their main properties. Finally, we investigate the strength of dynamical heterogeneity using the spatial variance of the local chemical potential and we correlate the latter to other features of the dynamical evolution.