コロキウム

We consider spatially periodic one-dimensional systems ruled by long-range interaction. Dynamics of such a system is described by using a distribution function governed by the Vlasov equation in the limit of large population. Any spatially homogeneous states are stationary solutions to the Vlasov equation, and a central issue is stability of and bifurcation from homogeneous states. Bifurcation is continuous in general but discontinuous one is possible in an attractive system [1]. We demonstrate numerically that the discontinuous bifurcation is also possible in a repulsive system, a jump is very small however. The smallness of jump is analyzed through a self-consistent theory.

[1] Discontinuous codimension-two bifurcation in a Vlasov equation, Y. Y. Yamaguchi and J. Barre, Phys. Rev. E 107(5), 054203 (2023).