Zero-frequency Component Research Articles

Green Function Theory of the Two-Spin System

The exact solution of the two-spin Heisenberg model with an external field is obtained by means of a Green function technique. The results are compared with an approximate solution of Patterson and Southwell in which a Tyablikov decoupling approximation is used. The special problem associated with the calculation of the zero-frequency component of the correlation function is also discussed.

Anomalous Diffusion in a Weakly Turbulent Plasma

A given spectrum of plasma oscillations, representing a state of weak turbulence, is considered in a uniform Vlasov plasma in a strong magnetic field. The parallel velocity and transverse spatial diffusion coefficients for thermal particles are found by studying the motion of a test particle. Diffusion results from the zero-frequency component of the electric field seen by the test particle. Two nonlinear processes contribute to this component: modification of the field seen by the test particle by high-frequency modulation of its velocity, and excitation of low-frequency ``virtual waves'' by nonresonant mode coupling. The latter effect dominates ion diffusion, increasing it by the factor (mi/me)2; for electrons, the two effects almost cancel, decreasing the diffusion by the factor (kλD)4. Thus the low-frequency virtual waves must not be neglected in estimating anomalous diffusion or heating associated with a given high-frequency spectrum.