Mean squared displacement

• abstract: In statistical mechanics, the mean squared displacement (MSD, also mean square displacement or average squared displacement) is the most common measure of the spatial extent of random motion; in some way it is often enlightening to think of the MSD as the amount of the system "explored" by the random walker. It prominently appears in the Debye-Waller factor (describing vibrations within the solid state) and in the Langevin equation (describing diffusion of a Brownian particle).

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