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This Lorenzian is cut off at large frequencies, of orders of γS γI/a3 (where a is the lattice constant or, more generally, the minimum possible distance between the I and S spins). However, since the I spins are diluted, n1/a3, this cutoff is far beyond the range of frequencies considered here and can be taken as infinity. Correspondingly, the exponential decay [Eq. 6] of Mx (t) sets in after some short transition time (of order of a3/γS γI), but this short time scale is negligible for our purposes. In the same way, the distribution 7 has a cutoff at very large b, of orders of γS γI/a3, which can be neglected at the energy/time scales considered in our work.
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This Lorenzian is cut off at large frequencies, of orders of γS γI/a3 (where a is the lattice constant or, more generally, the minimum possible distance between the I and S spins). However, since the I spins are diluted, n1/a3, this cutoff is far beyond the range of frequencies considered here and can be taken as infinity. Correspondingly, the exponential decay [Eq. 6] of Mx (t) sets in after some short transition time (of order of a3/γS γI), but this short time scale is negligible for our purposes. In the same way, the distribution 7 has a cutoff at very large b, of orders of γS γI/a3, which can be neglected at the energy/time scales considered in our work.
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