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

A spectral solution method is proposed to solve a previously 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 a 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.