Weak Ergodicity Breaking in Single-Particle Dynamics

2008 ◽  
pp. 365-391 ◽  
Author(s):  
E. Barkai
Keyword(s):  
Single Particle ◽  
Particle Dynamics ◽  
Weak Ergodicity ◽  
Weak Ergodicity Breaking ◽  
Ergodicity Breaking

scholarly journals Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Long Shi ◽  
Aiguo Xiao
Keyword(s):  
Brownian Motion ◽  
Continuous Time ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Weak Ergodicity ◽  
Normal Diffusion ◽  
Weak Ergodicity Breaking ◽  
The Mean ◽  
Ergodicity Breaking

We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.

scholarly journals Time-average based on scaling law in anomalous diffusions

2015 ◽  
Vol 29 (13) ◽  
pp. 1550059 ◽  
Author(s):  
Hyun-Joo Kim
Keyword(s):  
Single Molecule ◽  
Scaling Law ◽  
Lag Time ◽  
Markovian Model ◽  
Weak Ergodicity ◽  
Single Molecule Tracking ◽  
Memory Enhancement ◽  
Weak Ergodicity Breaking ◽  
Time Average ◽  
Ergodicity Breaking

To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions, we have suggested the time-averaged mean squared displacement (MSD) [Formula: see text] with an integral interval depending linearly on the lag time τ. For the continuous time random walk describing a subdiffusive behavior, we have found that [Formula: see text] like that of the ensemble-averaged MSD, which makes it be possible to measure the proper exponent values through time-average in experiments like a single molecule tracking. Also, we have found that it has originated from the scaling nature of the MSD at an aging time in anomalous diffusion and confirmed them through numerical results of the other microscopic non-Markovian model showing subdiffusions and superdiffusions with the origin of memory enhancement.

scholarly journals Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Carlo Manzo ◽  
Juan A. Torreno-Pina ◽  
Pietro Massignan ◽  
Gerald J. Lapeyre ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Living Cells ◽  
Weak Ergodicity ◽  
Weak Ergodicity Breaking ◽  
Ergodicity Breaking
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