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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.00984 |
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| _version_ | 1866918423794024448 |
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| author | Gavassino, Lorenzo |
| author_facet | Gavassino, Lorenzo |
| contents | We construct a family of exactly solvable relativistic kinetic theories in $1+1$ dimensions whose hydrodynamic sector continuously interpolates between Fick's and Cattaneo's laws of diffusion. The interpolation is controlled by a single parameter $a\in[0,1]$, which tunes the microscopic scattering dynamics from infinitely soft but infinitely frequent scatterings ($a=0$), reproducing standard diffusion, to maximally hard but finite-rate scatterings ($a=1$), yielding hyperbolic Cattaneo-type transport. For intermediate values of $a$, the dynamics combines frequent weak scatterings with rare strong randomizing events, providing a concrete microscopic realization of mixed diffusive-telegraphic behavior. Remarkably, the full quasinormal mode spectrum can be obtained analytically for all $a$. This allows us to track explicitly how purely diffusive modes continuously deform into damped propagating modes as the collision structure is varied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact interpolation between Fick and Cattaneo diffusion in relativistic kinetic theory Gavassino, Lorenzo Nuclear Theory High Energy Physics - Theory Mathematical Physics We construct a family of exactly solvable relativistic kinetic theories in $1+1$ dimensions whose hydrodynamic sector continuously interpolates between Fick's and Cattaneo's laws of diffusion. The interpolation is controlled by a single parameter $a\in[0,1]$, which tunes the microscopic scattering dynamics from infinitely soft but infinitely frequent scatterings ($a=0$), reproducing standard diffusion, to maximally hard but finite-rate scatterings ($a=1$), yielding hyperbolic Cattaneo-type transport. For intermediate values of $a$, the dynamics combines frequent weak scatterings with rare strong randomizing events, providing a concrete microscopic realization of mixed diffusive-telegraphic behavior. Remarkably, the full quasinormal mode spectrum can be obtained analytically for all $a$. This allows us to track explicitly how purely diffusive modes continuously deform into damped propagating modes as the collision structure is varied. |
| title | Exact interpolation between Fick and Cattaneo diffusion in relativistic kinetic theory |
| topic | Nuclear Theory High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.00984 |