Velocity of a perturbation in infinite lattice systems

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

“…In [17], Marchioro, Pellegrinotti, Pulvirenti, and Triolo considered anharmonic systems in thermal equilibrium and proved that, after time t, the influence of local perturbations becomes negligible at distances larger than t 4/3 . These bounds were recently improved in [8] by Buttà, Caglioti, Di Ruzza, and Marchioro, who proved that after time t local perturbations of thermal equilibrium are exponentially small in log 2 t at distances larger than t log α t.…”

Probing unitary two-time correlations in a neutral atom quantum simulator

“…5 We will now further bound the norm of the commutator in (38) in two different ways, and take the minimum of those two bounds and the trivial bound (37) as our final estimate of the error. 5 Had we removed H i from H in (25) (39) in (38) one obtains the error bound…”

On the Propagation of a Perturbation in an Anharmonic System

“…The general case seems too difficult, while for systems in thermal equilibrium a reasonable estimate has been obtained in Ref. [22]: the influence of the perturbation is exponentially small in time for distances |i − j| > t 4/3 .…”

“…For harmonic oscillators or bounded rotators it has been proved in Ref. [22] that this influence becomes negligible when |i − j| > ct, for some c which thus gives a bound of the velocity of propagation of the perturbation.…”

“…Following Ref. [22], we use the Poisson brackets to this purpose, by analogy with a similar problem in the quantum case previously studied in Ref. [18].…”