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We assume that the interaction can be tuned so that zero interaction is accessible. If this is experimentally not possible, no jump in the mathematical sense will occur in one dimension because even a small interaction implies a continuous MD. But the deviation in the sense of a L2 norm from a real jump tends to zero for vanishing interaction, so that for practical purposes, i.e., measurements with finite resolution, this fundamental aspect will not dominate.
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We assume that the interaction can be tuned so that zero interaction is accessible. If this is experimentally not possible, no jump in the mathematical sense will occur in one dimension because even a small interaction implies a continuous MD. But the deviation in the sense of a L2 norm from a real jump tends to zero for vanishing interaction, so that for practical purposes, i.e., measurements with finite resolution, this fundamental aspect will not dominate.
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