Single-file diffusion is referred to the motion of many interacting particles in one-dimensional channel which are so narrow that the particles can not pass each other, and as a result their sequence is preserved over time. Since its introduction more than 50 years ago, in modelling ion transport through cell membranes, the single-file diffusion has been observed in a wide variety of systems, e.g. diffusion of large molecules in zeolites, carrier migration in super ionic conductors, sliding of proteins along DNA, and many more.The characteristic feature of single-file diffusion is that, the variance of the displacement of a tracer particle at a time much larger than the mean collision time, scales as the square-root of time, compared to the linear dependence in normal diffusion. This sub-diffusive scaling has been demonstrated in a number of experimental realization.
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