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Question: n particles diffuse in one dimension in the potential ux...

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N particles diffuse in one dimension in the potential U(x) = ax2, with a > 0. (For example, such a potential could be provided by a line-shaped optical tweezer trap.) The particles have diffusion constant D

. a. Find the steady-state concentration,c0(x). At time t = 0, the potential is suddenly switched off (that is, a is set to zero).

b. What is the net particle flux just before and just after t=0?

c. What is the concentration c(x, t) for t > 0?

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