Non-equilibrium dynamics in quantum field theory at high density: the tsunami

TL;DR

This paper investigates the out-of-equilibrium dynamics of a dense relativistic quantum fluid in scalar field theory, revealing phenomena like dynamical symmetry restoration/breaking, out of equilibrium Goldstone bosons, and non-thermal equations of state.

Contribution

It provides a detailed analysis of the non-equilibrium evolution, symmetry phenomena, and correlation functions in high-density quantum field theory, including the role of Goldstone bosons and initial conditions.

Findings

Symmetry can be dynamically restored or broken out of equilibrium.

Goldstone bosons can exist without thermalization, showing scaling behaviour.

The equation of state depends on initial conditions and resembles radiation in broken symmetry cases.

Abstract

The dynamics of a dense relativistic quantum fluid out of thermodynamic equilibrium is studied in the framework of the Phi^4 scalar field theory in the large N limit. The time evolution of a particle distribution in momentum space (the tsunami) is computed. The effective mass felt by the particles in such a high density medium equals the tree level mass plus the expectation value of the squared field. The case of negative tree level squared mass is particularly interesting. In such case dynamical symmetry restoration as well as dynamical symmetry breaking can happen. Furthermore, the symmetry may stay broken with vanishing asymptotic squared mass showing the presence of out of equilibrium Goldstone bosons. We study these phenomena and identify the set of initial conditions that lead to each case. We compute the equation of state which turns to depend on the initial state. Although the system does not thermalize, the equation of state for asymptotically broken symmetry is of radiation type. We compute the correlation functions at equal times. The two point correlator for late times is the sum of different terms. One stems from the initial particle distribution. Another term accounts for the out of equilibrium Goldstone bosons created by spinodal unstabilities when the symmetry is asymptotically broken.Both terms are of the order of the inverse of the coupling for distances where causal signals can connect the two points. The contribution of the out of equilibrium Goldstones exhibits scaling behaviour in a generalized sense.