TY - JOUR

T1 - Packets of Diffusing Particles Exhibit Universal Exponential Tails

AU - Barkai, Eli

AU - Burov, Stanislav

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/2/14

Y1 - 2020/2/14

N2 - Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function P(X,t) of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to exponential decay (with logarithmic corrections) of P(X,t). This universal behavior also holds for short times, a fact that makes experimental observations readily achievable.

AB - Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function P(X,t) of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to exponential decay (with logarithmic corrections) of P(X,t). This universal behavior also holds for short times, a fact that makes experimental observations readily achievable.

UR - http://www.scopus.com/inward/record.url?scp=85080909830&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.124.060603

DO - 10.1103/PhysRevLett.124.060603

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C2 - 32109131

SN - 0031-9007

VL - 124

JO - Physical Review Letters

JF - Physical Review Letters

IS - 6

M1 - 060603

ER -