[Submitted on 23 Feb 2026] (cross-list from math-ph)
Lorentz-boosted diffusion: initial value formulation and exact solutions
It is well known that the diffusion equation, when treated as a stand-alone partial differential equation, exhibits exponential instabilities in boosted frames, which render the corresponding initial-value problem ill-posed. Recently, however, it was shown that Fick-type diffusion arises as the exact hydrodynamic sector of relativistic Fokker-Planck kinetic theory. In this work, we exploit this kinetic embedding to formulate a modified initial-value problem for one-dimensional Lorentz-boosted diffusion. We show that the resulting dynamics are well posed both forward and backward in time, provided the boosted density profiles admit a kinetic-theory realization. Such profiles form a space of band-limited functions, within which the evolution can be expressed as a discrete superposition of spatially sampled initial data, weighted by a Shannon-Whittaker-type Green function defined on the full Minkowski plane. The Green function is obtained in closed analytic form.
- Comments:
- 13 pages, 5 figures, published in PRD (see https://journals.aps.org/prd/abstract/10.1103/k646-mgz5)
- Subjects:
- Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics — Theory (hep-th); math.MP (math.MP); Nuclear Theory (nucl-th)
- arXiv:
- 2602.21254 [pdf]