Proses difusi relativistik melalui persamaan langevin dan fokker-planck

Arista Romadani(1*), Muhammad Farchani Rosyid(2)

(1) Fakultas Sains dan Teknologi, UIN Maulana Malik Ibrahim Malang
(2) Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Gadjah Mada
(*) Corresponding Author


Brownian motion theory is always challenging how to describe diffusion phenomena with the main issue is how to extend the classical theory of Brownian motion to the special relativity framework. In this study, we formulated dynamics and distribution of a Brownian particle in relativistic framework by using Langevin and Fokker-Planck equation. By representing Brownian particle dynamics by Langevin equation, the velocity curves  were dependent on the presence of viscous friction coefficient (heat bath), and were used generalized in special relativity theory, A relativistic Langevin equation reduces to the classical theory at low velocities. Likewise, the distribution of Brownian particles is represented  as a stationary solution of the relativistic Fokker-Planck equation. From numerical results, we found that the probability density in the relativistic Fokker-Planck equation for  was reduced to the standard Fokker-Planck equation in Netownian classical theory. For  the calculation result showed that the Hanggi-Klimontovich approach has a consistent result to the relativistic Maxwell distribution. This work could open a promising interpretation to formulate the diffusion phenomena into general relativity theory.


Brownian; relativity; Langevin; Fokker-Planck; diffusion

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