25 May 2004 Memory in diffusive systems
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Proceedings Volume 5467, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II; (2004) https://doi.org/10.1117/12.546351
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain
Abstract
The classical rate equations for the concentration p(x,t) or the probability density in the diffusion-limited regime are extended by including non-Markovian terms. We present analytical and numerical results for a whole class of evolution models with conserved p, where the underlying equations are of convolution type with temporally and spatially varying memory kernels. Based on our recent studies in the reaction-limited case with memory, we study now the influence of time and spatial couplings. Due to the balance between the conventional diffusive current and the additional force, originated by the feedback, the system exhibits a non-trivial stationary solution which depends on both the initial distribution and the memory strength. For a non-linear memory kernel of KPZ-type we get an asymptotic exact solution. Although the mean square displacement offers ultimately diffusion, the distribution function is determined by the memory strength, too. Differences to diffusion are observed in higher order cumulants. For an arbitrary memory kernel we find a criteria which enables us to get a non-trivial stationary solution.
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Steffen Trimper, Knud Zabrocki, "Memory in diffusive systems", Proc. SPIE 5467, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II, (25 May 2004); doi: 10.1117/12.546351; https://doi.org/10.1117/12.546351
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