Analytical derivation of diffusion coefficient for two-dimensional inviscid point-vortex system in negative absolute temperature

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Large-scale structure formation in vortex dynamics is a ubiquitous phenomenon, for example, Jupiter's Great Red Spot and eddies in Naruto Channel. However, the detailed mechanism is still unknown. Our final goal is to understand the dynamical mechanism of the vortex structure formation observed in the two-dimensional point vortex system at negative temperature which is first introduced by Onsager. As many research results predict that a key feature to understand the structure formation may be a diffusion process, the diffusion coefficient for the point vortex system has been investigated quantitatively. Obtained formula is an extension of the well-known Kubo formula. The result indicates that the diffusion coefficient is proportional to 1/N and the value goes to zero in the thermodynamic limit.