{"title":"Spectral eigenfunction decomposition of a Fokker–Planck operator for relativistic heavy-ion collisions","authors":"A. Rizzi, G. Wolschin","doi":"10.1140/epja/s10050-024-01410-7","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":786,"journal":{"name":"The European Physical Journal A","volume":"60 9","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epja/s10050-024-01410-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal A","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epja/s10050-024-01410-7","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
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Abstract
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.
期刊介绍:
Hadron Physics
Hadron Structure
Hadron Spectroscopy
Hadronic and Electroweak Interactions of Hadrons
Nonperturbative Approaches to QCD
Phenomenological Approaches to Hadron Physics
Nuclear and Quark Matter
Heavy-Ion Collisions
Phase Diagram of the Strong Interaction
Hard Probes
Quark-Gluon Plasma and Hadronic Matter
Relativistic Transport and Hydrodynamics
Compact Stars
Nuclear Physics
Nuclear Structure and Reactions
Few-Body Systems
Radioactive Beams
Electroweak Interactions
Nuclear Astrophysics
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