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arXiv · 2601.19474

The quasi-normal modes of relativistic Fokker-Planck kinetic theory

Lorenzo Gavassino
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Abstract

Employing the well-known unitary equivalence between Fokker-Planck operators and Schr\"odinger Hamiltonians, we compute the quasi-normal-mode spectrum of ultrarelativistic kinetic theories with momentum-space diffusion. We show that the collision operator reduces to a Dirac-delta Schr\"odinger problem in one spatial dimension, and to a Coulomb Schr\"odinger operator with hydrogenic spectrum in three dimensions. Finite spatial wavenumber appears as a perturbation of the associated quantum potential. The hydrodynamic mode is found to obey exact Fick-type diffusion at all real wavenumbers, whereas relativistic kinematics generically produces a continuous ballistic band in the non-hydrodynamic sector, a feature absent in the Newtonian regime.

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Lorenzo Gavassino. 2026-01-27. The quasi-normal modes of relativistic Fokker-Planck kinetic theory. https://doi.org/10.1103/6vfx-8kmm

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