Relaxation, frequency shifts and other phenomena at the transition between diffusion and ballistic motion

Abstract

There are many fields where the transition from diffusive to ballistic motion is important. Here we deal with relaxation processes in nmr in gases. Correlation functions for trajectory variables (position and velocity) valid across this transition are known for several geometries in the case of specular wall reflections. In this work we show that the conditional probability density p(r,t|r_0,t_0) for a random walk satisfies the telegrapher's equation and present an analytic solution for this function. We will use it for calculating the relaxation due to an axion mediated force and a magnetic dipole impurity.

arXiv comment10 pages, 4 figures first results

References in corpus (3)

• Relaxation of spins due to a magnetic field gradient, revisited; Identity of the Redfield and Torrey theories
• Spin relaxation and linear-in-electric-field frequency shift in an arbitrary, time-independent magnetic field
• Electric dipole moment searches: Effect of linear electric field frequency shifts induced in confined gases, II

Cited by in corpus (1)

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