On the Regime of Localized Excitations for Disordered Oscillator Systems
Mathematical Physics
2022-10-13 v1 math.MP
Spectral Theory
Abstract
We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with arbitrarily large energy density. We prove zero-velocity Lieb-Robinson bounds for the dynamics of Weyl operators as well as for position and momentum operators restricted to this regime. Dynamical localization is also shown in the form of quasi-locality of the time evolution of local Weyl operators and through exponential clustering of the dynamic correlations of states with localized excitations.
Keywords
Cite
@article{arxiv.1810.12769,
title = {On the Regime of Localized Excitations for Disordered Oscillator Systems},
author = {Houssam Abdul-Rahman and Robert Sims and Günter Stolz},
journal= {arXiv preprint arXiv:1810.12769},
year = {2022}
}