Brownian motion in a magnetic field and in the presence of additional external forces
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| Format: | Artículo científico |
| Language: | en |
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Sociedad Mexicana de Física A.C.
2008
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| author | J.I. Jiménez-Aquino |
| author_facet | J.I. Jiménez-Aquino |
| contents | Brownian motion in a magnetic field and in the presence of additional external forces J.I. Jiménez-Aquino M. Romero-Bastida A.C. Pérez-Guerrero Noyola Física, Astronomía y Matemáticas Planck Kramers (FP) Fokker (FPK) Fokker Our purpose in this paper is to solve exactly the Fokker-Planck-Kramers equation of a charged particle (heavy-ion) embedded in a fluid and under the influence of mechanical and electromagnetic forces. In this work the magnetic field is assumed to be constant and pointing along any direction of a Cartesian reference frame; the mechanical and electrical forces are both space-independent, but in general time- dependent. Our proposal relies upon two transformations of the Langevin equation associated with the charged particle’s phase-space (r, u). The first one is a fixed rotation which transforms the (r, u)-coordinates into other (r , u )-coordinates, and makes it possible to re-orientate the magnetic field along an appropriate direction (say along the z -axis). The second one is a time-dependent rotation which transforms the (r , u )-coordinates into other (r , u )-coordinates, in which the resulting Langevin equation strongly resembles that of ordinary Brownian motion in the presence of external forces. Under these circumstances, the Fokker-Planck-Kramers equation can immediately be solved in the (r , u ) phase-space, following our methodology developed in Ref. 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028301013 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.54 |
| format | Artículo científico |
| id | redalyc_57028301013 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Brownian motion in a magnetic field and in the presence of additional external forces J.I. Jiménez-Aquino Física, Astronomía y Matemáticas Planck Kramers (FP) Fokker (FPK) Fokker Brownian motion in a magnetic field and in the presence of additional external forces J.I. Jiménez-Aquino M. Romero-Bastida A.C. Pérez-Guerrero Noyola Física, Astronomía y Matemáticas Planck Kramers (FP) Fokker (FPK) Fokker Our purpose in this paper is to solve exactly the Fokker-Planck-Kramers equation of a charged particle (heavy-ion) embedded in a fluid and under the influence of mechanical and electromagnetic forces. In this work the magnetic field is assumed to be constant and pointing along any direction of a Cartesian reference frame; the mechanical and electrical forces are both space-independent, but in general time- dependent. Our proposal relies upon two transformations of the Langevin equation associated with the charged particle’s phase-space (r, u). The first one is a fixed rotation which transforms the (r, u)-coordinates into other (r , u )-coordinates, and makes it possible to re-orientate the magnetic field along an appropriate direction (say along the z -axis). The second one is a time-dependent rotation which transforms the (r , u )-coordinates into other (r , u )-coordinates, in which the resulting Langevin equation strongly resembles that of ordinary Brownian motion in the presence of external forces. Under these circumstances, the Fokker-Planck-Kramers equation can immediately be solved in the (r , u ) phase-space, following our methodology developed in Ref. 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028301013 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.54 |
| title | Brownian motion in a magnetic field and in the presence of additional external forces |
| topic | Física, Astronomía y Matemáticas Planck Kramers (FP) Fokker (FPK) Fokker |
| url | https://www.redalyc.org/articulo.oa?id=57028301013 |