Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-08-07
Phys. Rev. E Rapid Communication 75, 060104(R) (2007)
Physics
Condensed Matter
Statistical Mechanics
5 pages
Scientific paper
10.1103/PhysRevE.75.060104
Once the problem of ensemble averaging is removed, correlations between the response of a single molecule to an external driving field $F$, with the history of fluctuations of the particle, become detectable. Exact analytical theory for the continuous time random walk and numerical simulations for the quenched trap model give the behaviors of the correlation between fluctuations of the displacement in the aging period $(0,t_a)$, and the response to bias switched on at time $t_a$. In particular in the dynamical phase where the models exhibit aging we find finite correlations even in the asymptotic limit $t_a \to \infty$, while in the non-aging phase the correlations are zero in the same limit. Linear response theory gives a simple relation between these correlations and the fractional diffusion coefficient.
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