Analytical solution of the nonlinear relativistic Boltzmann equation
Abstract We provide an exact analytical solution to the nonlinear relativistic Boltzmann equation for a homogeneous, anisotropically scattering massless gas. Utilizing a BKW-like trial solution, we cast the Boltzmann equation into a set of nonlinear coupled equations for scalar moments, based on whi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)066 |
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| _version_ | 1849238253040828416 |
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| author | Jin Hu |
| author_facet | Jin Hu |
| author_sort | Jin Hu |
| collection | DOAJ |
| description | Abstract We provide an exact analytical solution to the nonlinear relativistic Boltzmann equation for a homogeneous, anisotropically scattering massless gas. Utilizing a BKW-like trial solution, we cast the Boltzmann equation into a set of nonlinear coupled equations for scalar moments, based on which the analytical solution is derived. One remarkable feature of our analytical solution lies in the nontrivial scattering angle dependence. We also show that this analytical solution admits a stable fixed point corresponding to the equilibrium solution as long as the parameters are physically feasible. Furthermore, a clear correspondence between our solution and the BKW solution pertaining to nonrelativistic Maxwell molecules is established, thereby clarifying the non-existence of a BKW-type solution in the relativistic domain for massive particles. |
| format | Article |
| id | doaj-art-d0d07272167f4d4294521784bd192bcb |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d0d07272167f4d4294521784bd192bcb2025-08-20T04:01:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025711410.1007/JHEP07(2025)066Analytical solution of the nonlinear relativistic Boltzmann equationJin Hu0Department of Physics, Fuzhou UniversityAbstract We provide an exact analytical solution to the nonlinear relativistic Boltzmann equation for a homogeneous, anisotropically scattering massless gas. Utilizing a BKW-like trial solution, we cast the Boltzmann equation into a set of nonlinear coupled equations for scalar moments, based on which the analytical solution is derived. One remarkable feature of our analytical solution lies in the nontrivial scattering angle dependence. We also show that this analytical solution admits a stable fixed point corresponding to the equilibrium solution as long as the parameters are physically feasible. Furthermore, a clear correspondence between our solution and the BKW solution pertaining to nonrelativistic Maxwell molecules is established, thereby clarifying the non-existence of a BKW-type solution in the relativistic domain for massive particles.https://doi.org/10.1007/JHEP07(2025)066Finite Temperature or Finite DensityQuark-Gluon Plasma |
| spellingShingle | Jin Hu Analytical solution of the nonlinear relativistic Boltzmann equation Journal of High Energy Physics Finite Temperature or Finite Density Quark-Gluon Plasma |
| title | Analytical solution of the nonlinear relativistic Boltzmann equation |
| title_full | Analytical solution of the nonlinear relativistic Boltzmann equation |
| title_fullStr | Analytical solution of the nonlinear relativistic Boltzmann equation |
| title_full_unstemmed | Analytical solution of the nonlinear relativistic Boltzmann equation |
| title_short | Analytical solution of the nonlinear relativistic Boltzmann equation |
| title_sort | analytical solution of the nonlinear relativistic boltzmann equation |
| topic | Finite Temperature or Finite Density Quark-Gluon Plasma |
| url | https://doi.org/10.1007/JHEP07(2025)066 |
| work_keys_str_mv | AT jinhu analyticalsolutionofthenonlinearrelativisticboltzmannequation |