Spectral properties of correlation functions of fields with arbitrary position dependence in restricted geometries from the ballistic to the diffusive regimes

TL;DR

This paper develops a method to calculate the spectral properties of correlation functions for fields with arbitrary spatial dependence in confined geometries, covering ballistic, diffusive, and transition regimes, with applications to NMR relaxation.

Contribution

It introduces a unified approach to compute correlation spectra in bounded regions for particles undergoing different transport regimes, bridging ballistic and diffusive behaviors.

Findings

Spectral calculations valid for 2D and 3D geometries.

Applicable across ballistic, diffusive, and transition regimes.

Relevance demonstrated for NMR relaxation processes.

Abstract

The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as seen by particles moving through the fields in regions bounded by specularly reflecting walls valid for diffusive and ballistic motion as well as the transition region in between for motion in 2 and 3 dimensions. Applications to relaxation in nmr are discussed.