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Spatial instabilities in a cloud of cold atoms

Dense cold atomic clouds have been shown to be similar to plasmas. Previous studies showed that such clouds exhibit instabilities induced by long-range interactions. However they did not describe the spatial properties of the dynamics. In this Letter, we study experimentally the spatial nature of stochastic instabilities and find out that the dynamics is localized. Data are analyzed both in the spectral domain and in the spatial domain (principal component analysis). Both methods fail to describe the dynamics in terms of eigenmodes, showing that space and time are not separable.