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Which notion of energy for bilinear quantum systems?* *This work has been partially supported by INRIA Nancy-Grand Est. Second and third authors were partially supported by French Agence National de la Recherche ANR “GCM” program “BLANC-CSD”, contract number NT09-504590. The third author was partially supported by European Research Council ERC StG 2009 “GeCoMethods”, contract number 239748.

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