Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems
arXiv:1902.05486 · doi:10.1103/PhysRevLett.122.180602
Abstract
We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the sparseness of the network. We derive a Lieb-Robinson bound on the speed of propagation across the classical network, which allows us to estimate the timescale at which the quantum system equilibrates. The bound contains a parameter that quantifies the degree of locality of the Hamiltonian and the observable. Locality was disregarded in earlier studies of equilibration times, and is believed to be a key ingredient for making contact with the majority of physically realistic models. The more local the Hamiltonian and observables, the longer the equilibration timescale predicted by the bound.
arXiv comment5+4 pages, 3+3 figures
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