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- W2024790843 abstract "Using the path-integral method, we derive the analytical solution for the following one-dimensional diffusion in random media: ensuremath{partial}P(x,t)/ensuremath{partial}t=D[${mathrm{ensuremath{partial}}}^{2}$P(x,t)/ensuremath{partial}${mathit{x}}^{2}$]+ensuremath{lambda}V(x)P(x,t) , where V is a white-noise Gaussian potential. A quantity ensuremath{tau}=(16D/9${ensuremath{lambda}}^{4}$${)}^{1/3}$ is introduced for the time scale. When the diffusion time tensuremath{ll}ensuremath{tau}, the behavior of the average 〈P(x,t)〉 is essentially diffusive. When tensuremath{gg}ensuremath{tau}, the random potential plays a dominant role, and the average 〈P(x,t)〉 tends to [${ensuremath{lambda}}^{4}$${mathit{t}}^{5/2}$/8(ensuremath{pi}${mathit{D}}^{3}$${)}^{1/2}$]exp[(${ensuremath{lambda}}^{4}$${mathit{t}}^{3}$/48D) (1-${mathit{x}}^{2}$/2Dt)]. t)]." @default.
- W2024790843 created "2016-06-24" @default.
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- W2024790843 date "1991-05-01" @default.
- W2024790843 modified "2023-09-26" @default.
- W2024790843 title "Path-integral approach to diffusion in random media" @default.
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- W2024790843 doi "https://doi.org/10.1103/physreva.43.5284" @default.
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