2019/02/28 by Daniel Nickelsen, Michael Kästner, Michael Kastner
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Geometry #Hamiltonian (control theory) #Hilbert space #Locality #Mathematical analysis #Mathematics #Observable #Parameter space #Physics #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Quantum system #Statistical physics #Upper and lower bounds #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevlett.122.180602
published as Phys. Rev. Lett. 122, 180602 (2019) · 5+4 pages, 3+3 figures
openalex publication_date 2019/05/10 · arxiv created 2019/05/11 · arxiv updated 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 it 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.