Lorentz-boosted diffusion: initial value formulation and exact solutions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914349669416960 |
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| author | Gavassino, Lorenzo |
| author_facet | Gavassino, Lorenzo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_21254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lorentz-boosted diffusion: initial value formulation and exact solutions Gavassino, Lorenzo Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Nuclear Theory 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. |
| title | Lorentz-boosted diffusion: initial value formulation and exact solutions |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2602.21254 |