Evolution speed in some coupled-spin models

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.

6 pages, 4 figures. Correction of numerous mistakes. One model made simpler. A superior algorithm used to solve the second example

References in corpus (3)

• Quantum limits to dynamical evolution
• The role of entanglement in dynamical evolution
• Speed-up through entanglement -- many-body effects in neutrino processes

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• Quantum break in high intensity gravitational wave interactions
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