In a series of papers Boyanovsky et al. have studied the evolution of an inflaton with a negative mass squared and a quartic self coupling using the Closed Time Path (CTP) formalism relevant for out-of-equilibrium dynamics. In this paper we comment on various aspects of these works. We first compare their approach to alternate approaches to study inflaton dynamics and point out that the use of the CTP formalism gives the same results as standard field theory in the Hartree and leading order large N approximations. We then rederive using the WKB approximation the large momentum mode functions of the inflaton needed for renormalisation and point out some differences with the previously obtained results. We also argue that the WKB approximation is valid only for large $k/a$ and not for large $k$ as apparently assumed in the above mentioned works. We comment on the renormalisation prescription adopted in these works and finally discuss how it differs from another more commonly used prescription.
Starting from kinetic theory, we obtain a nonlinear dissipative formalism describing the nonequilibrium evolution of scalar colored particles coupled selfconsistently to nonabelian classical gauge fields. The link between the one-particle distribution function of the kinetic description and the variables of the effective theory is determined by extremizing the entropy production. This method does not rely on the usual gradient expansion in fluid dynamic variables, and therefore the resulting effective theory can handle situations where these gradients (and hence the momentum-space anisotropies) are expected to be large. The formalism presented here, being computationally less demanding than kinetic theory, may be useful as a simplified model of the dynamics of color fields during the early stages of heavy ion collisions and in phenomena related to parton energy loss.
We study out-of-equilibrium dynamics of intense non-abelian gauge fields. Generalizing the well-known Nielsen-Olesen instabilities for constant initial color-magnetic fields, we investigate the impact of temporal modulations and fluctuations in the initial conditions. This leads to a remarkable coexistence of the original Nielsen-Olesen instability and the subdominant phenomenon of parametric resonance. Taking into account that the fields may be correlated only over a limited transverse size, we model characteristic aspects of the dynamics of color flux tubes relevant in the context of heavy-ion collisions.
We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated and we found that an effective temperature characterizes the slow modes of the system. The generic features of the evolution -- scaling laws -- are dictated by the ones of the single elastic line in a random environment.
In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of fourth order corrected version of the Fokker Planck equation and its analytical solution for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker Planck equation describe the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss It$hat{o}$, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion to describe the quantum description of randomness involved in the dynamics. We also present a computation to derive the expression for the measure of the stochastic non-linearity arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of Random Matrix Theory (RMT). Additionally, we discuss the role of out of time order correlation (OTOC) function to describe quantum chaos in the present non-equilibrium field theoretic setup. Finally, for completeness, we also provide a bound on the measure of quantum chaos arising due to the presence of stochastic non-linear dynamical interactions into the closed quantum system of the early universe in a completely model-independent way.
Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of QGP produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall explicitly demonstrate how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the $mu_B=0$ axis of the phase diagram. Within this setup, we show that we can quantitatively capture non-equilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modelling.