Abstract
In the kinetic theory of one-dimensional (1d) systems, the collision terms, such as the Boltzmann, Landau, and Balescu–Lenard collision terms, are identically zero, when the masses of all the particles are the same. This apparently implies that there is no relaxation in 1d systems. However, relaxations are observed in numerical simulations. The problem is due to an insufficient approximation in the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy. Zubarev and Novikov's theory [Teor. Mat. Fiz. 18 (1974) 78; ibid. 19 (1974) 237] for summing up all the contributions of all the orders of the BBGKY hierarchy is applied to 1d systems. As a result, the zero-collision term problem is solved. The unique properties of 1d systems are revealed.
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