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Description
When a Brownian particle moves too rapidly for the medium to effectively absorb its kinetic energy, the standard Einstein theory of diffusion with a constant viscous friction becomes invalidated. A natural description of this kind of Brownian dynamics is to take the friction as a decreasing even function of the particle's velocity. The stochastic equation of motion is formulated within this approach, in which a broad class of physically relevant functions describing the velocity-dependent friction is considered. An analytical formula for the diffusion coefficient $D$ is derived. It is shown that $D$ as a function of temperature $T$ may exhibit only three scaling types: (i) $D \propto T$, corresponding to the standard Einstein relation with velocity-independent friction; (ii) $D \propto T^{\alpha + 1}$, corresponding to a power-law decrease of the friction coefficient with the velocity of the particle, $\gamma(v) \propto 1/v^{2\alpha}$ at high $v$; (iii) $D \propto 1/\sqrt{T - T_c}$, corresponding to a Gaussian relation between friction coefficient and velocity.
| Keyword-1 | Surface diffusion |
|---|---|
| Keyword-2 | Long flights |
| Keyword-3 | Diffusion coefficient |
