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

TL;DR

This paper introduces a spectral eigenfunction decomposition method to solve the Fokker-Planck equation modeling partial thermalization in relativistic heavy-ion collisions, enhancing numerical accuracy and comparing results with LHC data.

Contribution

It presents a novel spectral solution approach for the Fokker-Planck equation in heavy-ion collision models, improving upon previous numerical methods.

Findings

Accurately models particle distributions in heavy-ion collisions.

Matches experimental data from ATLAS and ALICE collaborations.

Provides a more precise numerical solution method.

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.