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2
votes
1answer
102 views

Do electrons really diffuse when a temperature gradient is applied?

In many websites and books, it is generally said that the charge carriers, be it electrons or holes, diffuse through the considered material when a temperature gradient is applied. However I have ...
0
votes
1answer
18 views

Rotational diffusion - why isn't $\hat n(t)=\hat n(0) \; \forall t$?

Consider the rotational Langevin equation in the absence of an external force: $$\frac{d \hat n(t)}{dt} =\vec{\xi}(t) \times \hat n(t)$$ where $\vec \xi(t)$ is a Gaussian white noise and $\hat n(t) \...
1
vote
1answer
48 views

Uniqueness of the square-root of the diffusion matrix?

In the Langevin equation with hydrodynamic interactions the stochastic force on particle $a$ is: $$ \sqrt{2k_BT} A^{ab}_{ij} \xi^{b}_j(t)$$ where $\xi$ is a unit white noise. Here $ A^{ab}_{ij} $ is ...
8
votes
3answers
1k views

Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of ...
2
votes
0answers
1k views

Diffusion in a chemical potential gradient

I am having troubles to understand to connection between equilibrium and non equilibrium thermodynamics. I am studying a mixture of molecules $A,B,C$ and solvent $S$. The free energy $F$ is given by ...