Spectral eigenfunction decomposition of a Fokker-Planck operator for relativistic heavy-ion collisions

Abstract

A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the numerical solution. The particle's phase-space trajectories are treated as drift-diffusion stochastic process, leading to a Fokker-Planck equation (FPE) for the single-particle probability distribution function. The drift and diffusion coefficients are derived from the expected asymptotic states via appropriate fluctuation-dissipation relations, and the resulting FPE is then solved numerically using a spectral eigenfunction decomposition. The calculated time-dependent particle distributions are compared to Pb-Pb data from the ATLAS and ALICE collaborations at the Large Hadron Collider.

arXiv comment17 pages, 8 figures; submitted to Eur. Phys. J. A

References in corpus (24)

• Microscopic Models for Ultrarelativistic Heavy Ion Collisions
• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Collective flow and viscosity in relativistic heavy-ion collisions
• Radiative energy loss and $p_{\perp }$-broadening of high energy partons in nuclei
• The Color Glass Condensate
• Thermal phenomenology of hadrons from 200 AGeV S+S collisions
• Multiple Scattering, Parton Energy Loss and Modified Fragmentation Functions in Deeply Inelastic eA Scattering
• Extracting jet transport coefficient from jet quenching at RHIC and LHC
• Color Glass Condensate at the LHC: hadron multiplicities in $pp$, $pA$ and $AA$ collisions
• A transverse momentum differential global analysis of Heavy Ion Collisions
• Thermal equilibrium and statistical thermometers in special relativity
• Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory
• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• Baryon Stopping as a new Probe of Geometric Scaling
• Particle production sources at LHC energies
• Baryon stopping and saturation physics in relativistic collisions
• Scaling Behavior of $(N_{ch}{)}^{-1}d{N}_{ch}/d\eta$ at $\sqrt{s_{NN}}=130$ GeV by the PHOBOS Collaboration and Its Implication --A Possible Explanation Employing the Ornstein-Uhlenbeck Process--
• Centrality dependence of charged-hadron pseudorapidity distributions in PbPb collisions at LHC energies in the RDM
• Ultraviolet energy dependence of particle production sources in relativistic heavy-ion collisions
• Baryon stopping as a relativistic Markov process in phase space
• Beyond the thermal model in relativistic heavy-ion collisions
• Systematic investigation of the particle spectra in Heavy-ion collisions at the Large Hadron Collider
• Cylindrically symmetric diffusion model for relativistic heavy-ion collisions