Relaxation time approximation revisited and non-analytical structure in retarded correlators
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908789095006208 |
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| author | Hu, Jin |
| author_facet | Hu, Jin |
| contents | In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only the RTA with an energy-independent relaxation time can be justified in the case of hard interactions. Accordingly, we propose an alternative approach to restore the collision invariance lacking in traditional RTA. Besides, we provide a general statement on the non-analytical structures in the retarded correlators within the kinetic description. For hard interactions, hydrodynamic poles are the long-lived modes. Whereas for soft interactions, commonly encountered in relativistic kinetic theory, the gapless eigenvalue spectrum of linearized collision operator leads to gapless branch-cuts. We note that particle mass and inhomogeneous perturbations would complicate the above-mentioned non-analytical structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relaxation time approximation revisited and non-analytical structure in retarded correlators Hu, Jin High Energy Physics - Phenomenology Statistical Mechanics High Energy Physics - Theory Mathematical Physics Nuclear Theory In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only the RTA with an energy-independent relaxation time can be justified in the case of hard interactions. Accordingly, we propose an alternative approach to restore the collision invariance lacking in traditional RTA. Besides, we provide a general statement on the non-analytical structures in the retarded correlators within the kinetic description. For hard interactions, hydrodynamic poles are the long-lived modes. Whereas for soft interactions, commonly encountered in relativistic kinetic theory, the gapless eigenvalue spectrum of linearized collision operator leads to gapless branch-cuts. We note that particle mass and inhomogeneous perturbations would complicate the above-mentioned non-analytical structures. |
| title | Relaxation time approximation revisited and non-analytical structure in retarded correlators |
| topic | High Energy Physics - Phenomenology Statistical Mechanics High Energy Physics - Theory Mathematical Physics Nuclear Theory |
| url | https://arxiv.org/abs/2409.05131 |