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

2011/08/09 by Christopher Swank, C. M. Swank, Swank, C. M. +6
Engineering · Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Data Analysis #FOS: Physical sciences #Field-Flow Fractionation Techniques #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an) #cond-mat.stat-mech #physics.data-an

paper · pdf · doi:10.48550/arxiv.1108.4701

10 pages, 4 figures

arxiv created 2011/08/09 · openalex publication_date 2011/08/09 · arxiv updated 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Relaxation, frequency shifts and other phenomena at the transition between diffusion and ballistic motion
• Heuristic approach to trajectory correlation functions in bounded regions with Lambert scattering walls
• Conformal dispersion relation for mixed correlators
• Green's Dyadic, Spectral Function, Local Density of States, and Fluctuation Dissipation Theorem
• The S-matrix and boundary correlators in flat space