Spectral eigenfunction decomposition of a Fokker-Planck operator for relativistic heavy-ion collisions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916429445464064 |
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| author | Rizzi, A. Wolschin, G. |
| author_facet | Rizzi, A. Wolschin, G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral eigenfunction decomposition of a Fokker-Planck operator for relativistic heavy-ion collisions Rizzi, A. Wolschin, G. High Energy Physics - Phenomenology Nuclear Theory 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. |
| title | Spectral eigenfunction decomposition of a Fokker-Planck operator for relativistic heavy-ion collisions |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2408.12532 |