Time correlation of momentum in a collisionless plasma due to large fluctuations

The present paper shows that in one-dimensional collisionless plasma, due to large fluctuation, the time correlation of momentum asymptotically behaves inverse quadratically with time. The long-time tail correlation is closely related to nonlinear Landau damping M.B. Isichenko, Phys. Rev. Lett. 78, 2369 (1997)]. Furthermore, it reveals the possible relationship between fluctuation and dispersion. The result indicates that the long-time tail correlation can also occur in a reversibly dispersive system, where the previous theories are invalid. A by-product proves that it may be efficient to investigate the dispersive features of collisionless plasma in view of time correlation.