Geodesic
Statistical theory of thermal diffusion of Brownian particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 275-280

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Brownian motion in a fluid with a temperature gradient is investigated by using Luttinger's method of introducing auxiliary external fields. The Einstein relation for the diffusion coefficient $D=kT/\zeta$ and a similar relation for the thermal diffusion coefficient $D_\mathrm T=\displaystyle n_\sigma kT\frac{1+\eta/kT}{\zeta}$ are obtained ($n_\sigma$ is the density of the Brownian particles, $\zeta$ is the friction constant, and $\eta$ is the heat drag coefficient of the Brownian particles). The expressions obtained are compared with the results of other works on diffusion of Brownian particles in a fluid with a temperature gradient. 
@article{TMF_1969_1_2_a9,
     author = {A. G. Bashkirov},
     title = {Statistical theory of thermal diffusion of {Brownian} particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {275--280},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1969_1_2_a9/}
}
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A. G. Bashkirov. Statistical theory of thermal diffusion of Brownian particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 275-280. http://geodesic.mathdoc.fr/item/TMF_1969_1_2_a9/