Non-equilibrium dynamics of a scalar field with quantum backreaction

We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a fully thermalized system with a finite temperature. We identify the non-perturbative processes of parametric resonance and spinodal instability taking place during the reheating stage. In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function. Our methods can be easily adapted to simulate reheating at the end of inflation.

Holographic approach of the spinodal instability to criticality

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.

Crossing a large-N phase transition at finite volume

The existence of phase-separated states is an essential feature of infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the phase transition takes place, equilibrium homogeneous states are either metastable or suffer from a spinodal instability. In this range the stable states are inhomogeneous, phase-separated states. We use holography to investigate how this picture is modified at finite volume in a strongly coupled, four-dimensional gauge theory. We work in the planar limit, N → ∞, which ensures that we remain in the thermodynamic limit. We uncover a rich set of inhomogeneous states dual to lumpy black branes on the gravity side, as well as first- and second-order phase transitions between them. We establish their local (in)stability properties and show that fully non-linear time evolution in the bulk takes unstable states to stable ones.