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

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