The Convergence Problem Of Gradient Expansion In The Relaxation Time Approximation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916257143455744 |
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| author | Gangadharan, Reghukrishnan Roy, Victor |
| author_facet | Gangadharan, Reghukrishnan Roy, Victor |
| contents | We obtain a formal integral solution to the 3+1 D Boltzmann Equation in relaxation time approximation. The gradient series obtained from this integral solution contains exponentially decaying non-hydrodynamic terms. It is shown that this gradient expansion can have a finite radius of convergence under certain assumptions of analyticity. We then argue that, in the relaxation time model, proximity to local thermal equilibrium is not necessary for the system to be described by hydrodynamic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Convergence Problem Of Gradient Expansion In The Relaxation Time Approximation Gangadharan, Reghukrishnan Roy, Victor Nuclear Theory High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics We obtain a formal integral solution to the 3+1 D Boltzmann Equation in relaxation time approximation. The gradient series obtained from this integral solution contains exponentially decaying non-hydrodynamic terms. It is shown that this gradient expansion can have a finite radius of convergence under certain assumptions of analyticity. We then argue that, in the relaxation time model, proximity to local thermal equilibrium is not necessary for the system to be described by hydrodynamic equations. |
| title | The Convergence Problem Of Gradient Expansion In The Relaxation Time Approximation |
| topic | Nuclear Theory High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.10846 |