Strong correlations between fluctuations and response in aging transport

The correlations between the response of a random walker to an external driving field F switched on at time ta, with the particle's fluctuations in the aging period (0, ta) are investigated. Using the continuous time random walk and the quenched trap model, it is shown that these correlations remain finite even in the asymptotic limit ta →. Linear response theory gives a relation between the correlations, the fractional diffusion coefficient, and the field F, thus generalizing the Einstein relation. In systems which exhibit aging, fluctuations in the aging period can be used to statistically predict the nonidentical response of particles to an external field.