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The search for particle electric dipole moments (edm) is one of the bestplaces to look for physics beyond the standard model because the size of timereversal violation predicted by the standard model is incompatible with presentideas concerning the creation of the Baryon-Antibaryon asymmetry. As thesensitivity of these edm searches increases more subtle systematic effectsbecome important. We develop a general analytical approach to describe asystematic effect recently observed in an electric dipole moment experimentusing stored particles \cite{JMP}. Our approach is based on the relationshipbetween the systematic frequency shift and the velocity autocorrelationfunction of the resonating particles. Our results, when applied to well-knownlimiting forms of the correlation function, are in good agreement with both thelimiting cases studied in recent work that employed a numerical/heuristicanalysis. Our general approach explains some of the surprising results observedin that work and displays the rich behavior of the shift for intermediatefrequencies, which has not been previously studied.Comment: 25 pages, 4 figures New expanded and corrected version. Includes  study of the frequency shift at intermediate resonant frequencies. New vesion  has labelling of Fig. 3 corrected, and adds a calculation of the  position-velocity correlation function by a direct technique. Appendix added  with a new proof of egelstaff's velodity correlation function theore

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Detailed discussion of a linear electric field frequency shift induced in confined gases by a magnetic field gradient: Implications for neutron electric-dipole-moment experiments