Autocorrelation of the Rouse-GLE transient subdiffusion model.
rouse_acf(alpha, tau, K, dt, N, ...)Subdiffusion coefficient between 0 and 1.
Shortest timescale of memory kernel.
Number of relaxation modes.
Time between obserations.
Number of observations.
Additional arguments to pass to prony_acf().
Vector of autocorrelations.
The Rouse-GLE satisfies the integro-differential equation $$ F_t - \int_{-\infty}^t \gamma(t-s) \dot X_s ds = 0, $$ where \(acf_F(t) = k_B T \gamma(t)\) and $$ \gamma(t) = 1/K sum_{k=1}^K exp(-\lambda_k * t), \lambda_k = (k/K)^(1/alpha)/tau. $$
As the temperature \(T\) is not supplied, the output is only proportional to the autocorrelation, in the sense that ACF_X(t) = k_B * T * rouse_acf.