Mean Squared Displacement of the Rouse-GLE transient subdiffusion model.
rouse_msd(t, alpha, tau, K, ...)Vector of timepoints at which to calculate the MSD.
Subdiffusion coefficient between 0 and 1.
Shortest timescale of memory kernel.
Number of relaxation modes.
Additional arguments to pass to prony_msd().
Vector of mean square displacements.
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 $$ \gamma(t) = 1/K sum_{n=1}^K exp(-\lambda_n * t), \lambda_n = (n/K)^(1/alpha)/tau. $$
As the temperature \(T\) is not supplied, the output is only proportional to the MSD, in the sense that \(MSD_X(t) = (2 * k_B * T * K) * msd\).