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Journal Article

Diffusion in Curved Spacetimes

MPS-Authors
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Smerlak,  Matteo
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1104.3303
(Preprint), 206KB

NJoP_14_2_023019.pdf
(Any fulltext), 582KB

Supplementary Material (public)
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Citation

Smerlak, M. (2012). Diffusion in Curved Spacetimes. New Journal of Physics, 14: 023019. doi:10.1088/1367-2630/14/2/023019.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-4841-5
Abstract
Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and therefore provides a microscopic justification for his phenomenological heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of the mean square displacement of Brownian motion in static spacetimes. Beyond general relativity itself, this result has potential applications in analogue gravitational systems.