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Flux for a System with Infinite Globally Coupled Oscillators Driven by Temporal-Spatial Noises

The transport of a spatially periodic system with infinite globally coupled oscillators driven by temporal-spatial noises is investigated. The probability current shows that the correlation of the multiplicative noises with the space, the spatial asymmetry, and the coupling among the different oscillators are ingredients for the transport of particles. It is a new phenomenon that the correlation of the multiplicative noises with the space can induce the nonzero flux.