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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.00126 |
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| _version_ | 1866908605132832768 |
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| author | Gangadharan, Reghukrishnan Mitra, Sukanya Roy, Victor |
| author_facet | Gangadharan, Reghukrishnan Mitra, Sukanya Roy, Victor |
| contents | We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which form an infinite hierarchy, provide important insights about the system dynamics and the approach towards equilibrium for systems far from equilibrium. The momentum-dependent collision kernel couples moments through both the energy exponents and the angular dependence via various-order Legendre polynomials, resulting in an intricate system of infinitely coupled equations. A naive truncation of the coupled equations results in diverging moments at late times. We outline strategies for solving the coupled system, including a novel approach for managing the divergences and non-integer moments. We show a significant influence of momentum dependent relaxation time on the time evolution of the moments, particularly for higher-order moments and system with smaller shear viscosity over entropy density, emphasizing the importance of incorporating such dependence for a more accurate description of the system dynamics with low shear viscosity such as the quark-gluon-plasma produced in high-energy heavy-ion collisions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Approach Towards Equilibrium Through Momentum-Dependent Relaxation:Insights from Evolution of the Moments in Kinetic Theory Gangadharan, Reghukrishnan Mitra, Sukanya Roy, Victor Nuclear Theory We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which form an infinite hierarchy, provide important insights about the system dynamics and the approach towards equilibrium for systems far from equilibrium. The momentum-dependent collision kernel couples moments through both the energy exponents and the angular dependence via various-order Legendre polynomials, resulting in an intricate system of infinitely coupled equations. A naive truncation of the coupled equations results in diverging moments at late times. We outline strategies for solving the coupled system, including a novel approach for managing the divergences and non-integer moments. We show a significant influence of momentum dependent relaxation time on the time evolution of the moments, particularly for higher-order moments and system with smaller shear viscosity over entropy density, emphasizing the importance of incorporating such dependence for a more accurate description of the system dynamics with low shear viscosity such as the quark-gluon-plasma produced in high-energy heavy-ion collisions. |
| title | On the Approach Towards Equilibrium Through Momentum-Dependent Relaxation:Insights from Evolution of the Moments in Kinetic Theory |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2504.00126 |