Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects

Abstract

We consider a simple model for the diffusion of heavy quarks in a hot bath, modeling the latter by an ensemble of oscillators distributed accorded to either a thermal distribution or to an out-of-equilibrium distribution with a saturation scale. Within this model it is easy to introduce memory effects by changing the distribution of oscillators: we model these by introducing a gaussian distribution, $dN/d\omega$, which can be deformed continuously from a $\delta -$function giving a Markov dissipation to a broad kernel with memory. Deriving the equation of motion of the heavy quark in the bath we remark how dissipation comes out naturally as an effect of the back-reaction on the bath of oscillators. Moreover, the exact solution of this equation allows for the definition of a thermalization time as the time necessary to remove any memory of the initial condition. We find that the broadening the dissipative kernel while keeping the coupling fixed lowers the thermalization time. We also derive the fluctuation-dissipation theorem for the bath, and use this to estimate the kinematic regime in which momentum diffusion of the heavy quark dominates over drift: we find that diffusion is more important as long as $K_0/\mathcal{E}$ is small, where $K_0$ and $\mathcal{E}$ denote the initial energy of the heavy quark and the average energy of the bath respectively.

References in corpus (45)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Color Glass Condensate
• Green's Functions in the Color Field of a Large Nucleus
• How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
• Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
• Some Features of the Glasma
• Heavy-Quark Probes of the Quark-Gluon Plasma at RHIC
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions
• Gluon Production at High Transverse Momentum in the McLerran-Venugopalan Model of Nuclear Structure Functions
• Fundamental Aspects of Quantum Brownian Motion
• Nonperturbative Heavy-Quark Diffusion in the Quark-Gluon Plasma
• Extraction of Heavy-Flavor Transport Coefficients in QCD Matter
• Coherent gluon production in very high energy heavy ion collisions
• Heavy quark dynamics and hadronization in ultra-relativistic heavy-ion collisions: collisional versus radiative energy loss
• The initial gluon multiplicity in heavy ion collisions
• Directed Flow of Charm Quarks as a Witness of the Initial Strong Magnetic Field in Ultra-Relativistic Heavy Ion Collisions
• Toward a solution to the $R_{AA}$ and $v_2$ puzzle for heavy quarks
• Bose--Einstein Condensation and Thermalization of the Quark Gluon Plasma
• Open Heavy Flavor in QCD Matter and in Nuclear Collisions
• Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update
• Yang-Mills Radiation in Ultra-relativistic Nuclear Collisions
• Color Glass Condensate and Glasma
• Initial Singularity of the Little Bang
• Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
• Heavy flavours in AA collisions: production, transport and final spectra
• Heavy-flavor production and medium properties in high-energy nuclear collisions - What next?
• Gluon Transport Equation in the Small Angle Approximation and the Onset of Bose-Einstein Condensation
• Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions
• Effect of pre-equilibrium phase on $R_{AA}$ and $v_2$ of heavy quarks in heavy ion collisions
• Relativistic Langevin Dynamics in Expanding Media
• The cathode tube effect: heavy quarks probing the Glasma in p-Pb collisions
• Heavy Quarks in Turbulent QCD Plasmas
• Initial energy density and gluon distribution from the Glasma in heavy-ion collisions
• Heavy-flavour production in high-energy d-Au and p-Pb collisions
• Causal Baryon Diffusion and Colored Noise
• Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation
• Heavy quark diffusion in pre-equilibrium stage of heavy ion collisions
• Dilepton yields from Brown-Rho scaled vector mesons including memory effects
• Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
• Evolution of pressures and correlations in the Glasma produced in high energy nuclear collisions
• Diffusion of charm and beauty in the Glasma
• A Monte Carlo framework for noncontinuous interactions between particles and classical fields
• Memory effects in radiative jet energy loss

Cited by in corpus (4)

• Ballistic diffusion of heavy quarks in the early stage of relativistic heavy ion collisions at RHIC and LHC
• Diffusion of heavy quarks in the early stage of high-energy nuclear collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider
• Energy Loss Versus Energy Gain of Heavy Quarks in a Hot Medium
• Heavy Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium