Memory effects and thermodynamics in strong field plasmas

Abstract

We study the evolution of a strong field plasma using a quantum Vlasov equation with a nonMarkovian source term and a simple collision term, and calculate the time dependence of the energy-and number-density, and the temperature. The evolution of a plasma produced with RHIClike initial conditions is well described by a low density approximation to the source term. However, non-Markovian aspects should be retained to obtain an accurate description of the early stages of an LHC-like plasma.Preprint Number: ANL-PHY-9434-TH-99, Pacs Numbers: 12.38. Mh, 25.75.Dw, 05.20.Dd, 05.60.Gg At extreme temperature, hadronic matter undergoes a phase transition to an equilibrated quark gluon plasma.Estimates from phenomenological models and lattice-QCD indicate a critical temperature for this transition: T c ∼ 170 MeV, which corresponds to an energy density of 2-3 GeV/fm 3 . It is hoped that this plasma will be produced at the Relativistic Heavy-Ion Collider (RHIC) and/or the Large Hadron Collider (LHC) [1]. However, little is currently understood about the formation, equilibration and hadronisation of the plasma, and herein we focus on dynamical aspects of the pre-equilibrium phase.We employ a flux-tube model to explore the creation of a strong-field plasma and follow its evolution towards equilibrium. The model assumes that the collision of two heavy nuclei produces a strong background field and a region of high energy density, which decays via pair emission. The particles produced in this process are accelerated by the background field, providing a current and a field that opposes the background field. This is the backreaction process, which may result in plasma oscillations. For QED in an external field it has been studied via mean field methods and using a quantum Vlasov equation with a Schwinger-like source term [2]. Collisions between the particles damp the plasma oscillations and are necessary to equilibrate the plasma, and their effect has been modelled in the Vlasov equation approach [3][4][5][6].For strong fields, non-Markovian aspects of the particle production mechanism are very important [7,[9][10][11]. Herein we emphasise this, using a relativistic transport equation with the non-Markovian source term derived in Refs. [8][9][10] and explored in Refs. [11,12]. We apply it with impact energy densities of the scales anticipated at RHIC and LHC, and study the time evolution of the plasma's properties.We model the effect of the nucleus-nucleus collision by an external, spatially-homogeneous, time-dependent Coulomb-gauge vector potential, which defines the longitudinal direction: A µ = (0, 0, 0, A(t)). The kinetic equation describing fermion production in this external field is [8] where, in contrast to the Schwinger production rate, the source term here is momentum-and time-dependent:E(t) = −dA(t)/dt and e is an electric charge, with the dynamical phase and total energy, respectively,where ε ⊥ = m 2 + p 2 ⊥ is the transverse energy. m 2 ∼ Λ 2 QCD ∼ 0.2 GeV/fm sets a typical scale. The second term on the right-hand-s...

Plasma production and thermalisation in a strong field

“…(In the weak-field limit a time-local Schwinger-like source term is recovered.) Such a situation is plausible at RHIC and especially at LHC [2,15] where the anticipated initial energy densities are, respectively, ε ∼ 10-100 GeV/fm 3 and ε > ∼ 1 TeV/fm 3 . Another feature that is characteristic of the flux-tube production mechanism is the back-reaction phenomenon.…”

“…; e.g., Refs. [14,15], because it is manageable and better models the conditions produced by an URHIC. Clearly, just after the impact the parton number density is small and hence the time between successive collisions is large.…”

“…However, its complexity mitigates against its use in semi-quantitative, exploratory studies and hence herein we employ a simple RTA [14,15,18,19,20,21,22,23].…”

“…This phrase simply describes the fact that once the particles are produced they are accelerated and thereby generate a field that interferes with the collisional field that produced them. Plasma oscillations are then almost inevitable [16], although they can rapidly be damped if the thermalising collisions between particles are frequent [14,15,17,18,19,20,21,22,23].…”

“…Particle production by the flux tube is described by a source term and in quantum field theory that source term is non-Markovian [10,11,12,13,14,15]; i.e., essentially nonlocal in time. This feature can be important when the fields are strong.…”