The covariant Langevin equation of diffusion on Riemannian manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913559818010624 |
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| author | Diósi, Lajos |
| author_facet | Diósi, Lajos |
| contents | The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential equation is long sought after in both physics and mathematics. We show that the simplest covariant Stratonovich stochastic differential equation depending on the local orthogonal frame (cf. vielbein) becomes the desired covariant Langevin equation provided we impose an additional covariant constraint: the vectors of the frame must be divergence-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17314 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The covariant Langevin equation of diffusion on Riemannian manifolds Diósi, Lajos Statistical Mechanics General Relativity and Quantum Cosmology Mathematical Physics The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential equation is long sought after in both physics and mathematics. We show that the simplest covariant Stratonovich stochastic differential equation depending on the local orthogonal frame (cf. vielbein) becomes the desired covariant Langevin equation provided we impose an additional covariant constraint: the vectors of the frame must be divergence-free. |
| title | The covariant Langevin equation of diffusion on Riemannian manifolds |
| topic | Statistical Mechanics General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2310.17314 |