Analysis of the Relativistic Brownian Motion in Momentum Space
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| Format: | Artículo científico |
| Language: | en |
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Sociedade Brasileira de Física
2006
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| _version_ | 1876429451360731136 |
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| author | Kwok Sau Fa |
| author_facet | Kwok Sau Fa |
| contents | Analysis of the Relativistic Brownian Motion in Momentum Space Kwok Sau Fa Física, Astronomía y Matemáticas Fokker Planck equation Langevin equation Relativistic Brownian motion We investigate the relativistic Brownian motion in the context of Fokker-Planck equation. Due to the multiplicative noise term of the corresponding relativistic Langevin equation many Fokker-Planck equations can be generated. Here, we only consider the Ito, Stratonovich and Hänggi-Klimontovich approaches. We analyze the behaviors of the second moment of momentum in terms of temperature. We show that the second moment increases with the temperature T for all three approaches. Also, we present differential equations for more complicated averages of the momentum. In a specific case, in the Ito approach, we can obtain an analytical solution of the temporal evolution of an average of the momentum. We present approximate solutions for the probability density for all three cases. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413654035 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.36 |
| format | Artículo científico |
| id | redalyc_46413654035 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Analysis of the Relativistic Brownian Motion in Momentum Space Kwok Sau Fa Física, Astronomía y Matemáticas Fokker Planck equation Langevin equation Relativistic Brownian motion Analysis of the Relativistic Brownian Motion in Momentum Space Kwok Sau Fa Física, Astronomía y Matemáticas Fokker Planck equation Langevin equation Relativistic Brownian motion We investigate the relativistic Brownian motion in the context of Fokker-Planck equation. Due to the multiplicative noise term of the corresponding relativistic Langevin equation many Fokker-Planck equations can be generated. Here, we only consider the Ito, Stratonovich and Hänggi-Klimontovich approaches. We analyze the behaviors of the second moment of momentum in terms of temperature. We show that the second moment increases with the temperature T for all three approaches. Also, we present differential equations for more complicated averages of the momentum. In a specific case, in the Ito approach, we can obtain an analytical solution of the temporal evolution of an average of the momentum. We present approximate solutions for the probability density for all three cases. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413654035 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.36 |
| title | Analysis of the Relativistic Brownian Motion in Momentum Space |
| topic | Física, Astronomía y Matemáticas Fokker Planck equation Langevin equation Relativistic Brownian motion |
| url | https://www.redalyc.org/articulo.oa?id=46413654035 |