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Mathematical Physics
Title: Locality bounds for quantum dynamics at low energy
(Submitted on 4 Oct 2023 (v1), last revised 29 Mar 2024 (this version, v3))
Abstract: We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of lattice-regularized $H\propto p^{2k}$), the ``butterfly velocity" of particle motion at low energies has an upper bound that must scale as $E^{(2k-1)/2k}$, as expected from dimensional analysis. We generalize these results to obtain bounds on the typical velocities of particles in many-body systems with repulsive interactions, where for certain families of Hubbard-like models we obtain similar scaling.
Submission history
From: Andrew Osborne [view email][v1] Wed, 4 Oct 2023 14:42:51 GMT (24kb)
[v2] Mon, 12 Feb 2024 18:43:40 GMT (27kb)
[v3] Fri, 29 Mar 2024 16:47:21 GMT (27kb)
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