%0 Book Section %1 statphys23_0102 %A Aquino, J.I. Jimenez %A Romero-Bastida, M. %A Guerrero, A.C. Perez %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K fokker-planck langevin statphys23 topic-3 %T The Fokker-Planck equation of a Brownian particle in an electromagnetic field %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=102 %X The purpose of this work is to describe the diffusion process of heavy ions in a light gas in presence of an external electromagnetic field, by assuming a constant magnetic field pointing along an arbitrary direction $B=(B_x,B_y,B_z)$ and a general time-varying electric field $E(t)$. This process will be described through the Fokker-Planck (FP) equation associated with the corresponding Langevin equation. The exact solution of the FP equation can be found, by means of a transformation, through a time-dependent rotation matrix, of the associated Lagevin equation, which renders quite similar to that of the ordinary Brownian motion under the action of an external force. In this sense, the solution of the FP equation in the transformed velocity-space comes out immediately. We also use the same initial heavy-ion velocity Maxwellian distribution at temperature different from that of equilibrium, and around the mean velocity $u\rangle_0$, proposed by Ferrari Physica A 163, 596 (1990), to calculate a more general probability density. PACS numbers: 05.40.-a, 02.50.-r

@incollection{statphys23_0102, abstract = {The purpose of this work is to describe the diffusion process of heavy ions in a light gas in presence of an external electromagnetic field, by assuming a constant magnetic field pointing along an arbitrary direction ${\bf B}=(B_x,B_y,B_z)$ and a general time-varying electric field ${\bf E}(t)$. This process will be described through the Fokker-Planck (FP) equation associated with the corresponding Langevin equation. The exact solution of the FP equation can be found, by means of a transformation, through a time-dependent rotation matrix, of the associated Lagevin equation, which renders quite similar to that of the ordinary Brownian motion under the action of an external force. In this sense, the solution of the FP equation in the transformed velocity-space comes out immediately. We also use the same initial heavy-ion velocity Maxwellian distribution at temperature different from that of equilibrium, and around the mean velocity $\langle{\bf u}\rangle_0$, proposed by Ferrari [Physica A {\bf 163}, 596 (1990)], to calculate a more general probability density. PACS numbers: 05.40.-a, 02.50.-r}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Aquino, J.I. Jimenez and Romero-Bastida, M. and Guerrero, A.C. Perez}, biburl = {https://www.bibsonomy.org/bibtex/22236cce07e3e1ee5b051848d6e407374/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {fb4fbaa8292d559d3a35257e0e39d4ef}, intrahash = {2236cce07e3e1ee5b051848d6e407374}, keywords = {fokker-planck langevin statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:11.000+0200}, title = {The Fokker-Planck equation of a Brownian particle in an electromagnetic field}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=102}, year = 2007 }