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I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that take part in condensation? Or is it a property of the condensate?

Does anyone have a good explanation?

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You call the condensate 'scalar' when the atoms are spin-0. When instead atoms have a non trivial spin you talk about 'spinor condensates'.

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