Resonance behavior for the dynamical friction of a system in a trapping potential

Abstract

The kinetic energy fluctuation metric ${\mathrm{\ensuremath{\Omega}}}_{\mathbf{K}}(t)$ is modified to extract the dynamical friction in non-Markovian scenarios to circumvent Markovian scenarios. Dynamical friction is calculated from the ratio ${\mathrm{\ensuremath{\Omega}}}_{\mathbf{K}}(0)/{\mathrm{\ensuremath{\Omega}}}_{\mathbf{K}}(t)$, which obeys a universal scaling law. Both analytical and numerical results of a minimal non-Markovian model substantiate the validity of the modified kinetic energy fluctuation metric. We reveal that previous studies on the rates of relaxation in harmonically bounded proteins, which are somewhat larger than those resulting from the experimental fit, may have neglected non-Markovian effects. When applying the metric to a system subjected to thermal broadband colored noise in the harmonic potential, resonance phenomenon occurs. Specifically, dynamical friction varies nonmonotonically with the frequency of the harmonic potential. The optimal frequency inducing the strongest dynamical friction matches well with the peak frequency of power spectrum of thermal broadband colored noise. The system then approaches to equilibrium rapidly. For an acoustic phonon spectrum, the resonance for dynamical friction provides further insight as to why complete thermalization only occurs when the particle frequency of the system is within a certain range of the environment particle frequencies. This is because the closer the potential frequency is to the central value of the range of frequencies, the stronger is the dynamical friction induced.