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Main Author: Gavassino, Lorenzo
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.00984
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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