Abstract
We investigate the time evolution of some models with $N$ spins and pairwise couplings, for the case of large $N$, in order to compare evolution times with ``speed-limit'' minima derived in the literature. Both in a (symmetric) case with couplings of the same strength between each pair and in a case of broken symmetry, the times necessary for evolution to a state in which the simplest initial state has evolved into a nearly orthogonal state are proportional to $1∕N$, as is the speed limit time. However, the coefficient in the broken symmetry case comes much closer to the speed limit value. Introducing a different criterion for evolution speed, based on macroscopic changes in occupation, we find a corresponding enhancement in rates in the asymmetric case as compared to the symmetric case.
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