The intermediate scattering function for quasi-elastic scattering in the presence of memory friction

TL;DR

This paper derives an analytical expression for the intermediate scattering function of a particle with memory friction, confirmed by simulations, revealing how memory timescales influence scattering line shapes and potential for inferring friction kernels.

Contribution

It provides the first analytical expression for the intermediate scattering function with exponential memory friction and validates it through numerical simulations.

Findings

Memory timescale affects short-time correlations and line shape amplitudes.

Long-time exponential tail decay rate remains unchanged by memory effects.

Sensitivity of line shape amplitudes to memory decay time enables inference of friction kernels.

Abstract

We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin Equation, with exponential memory friction. Numerical simulations based on an extended phase space method confirm the analytical results. The simulated trajectories provide qualitative insight into the effect that introducing a finite memory timescale has on the analytical line shapes. The relative amplitude of the long-time exponential tail of the line shape is suppressed, but its decay rate is unchanged, reflecting the fact that the cutoff frequency of the exponential kernel affects short-time correlations but not the diffusion coefficient which is defined in terms of a long-time limit. The exponential sensitivity of the relative amplitudes to the decay time of the chosen memory kernel is a very strong indicator for the prospect of inferring a friction kernel and the physical insights from experimentally measured intermediate scattering functions.