Show simple item record

dc.contributor.authorBru, J.-B. 
dc.contributor.authorde Siqueira Pedra, W.
dc.description.abstractWe generalize to multi-commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate time-dependent multi-commutators for interacting fermions. Lieb–Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of the dynamics of quantum particles with interactions which are non-vanishing in the whole space and possibly time-dependent. To illustrate this, we prove that the bounds for multi-commutators of order three yield existence of fundamental solutions for the corresponding non-autonomous initial value problems for observables of interacting fermions on lattices. We further show how bounds for multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting fermions to external perturbations. All results also apply to quantum spin systems, with obvious modifications. However, we only explain the fermionic case in detail, in view of applications to microscopic quantum theory of electrical conduction discussed here and because this case is technically more involved.en_US
dc.description.sponsorshipFAPESP under Grant 2013/13215-5 Basque Government through the grant IT641-13 SEV-2013-0323 MTM2014-53850en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectLieb–Robinson Boundsen_US
dc.subjectResponse theoryen_US
dc.subjectQuantum spinen_US
dc.subjectEvolution equationsen_US
dc.subjectConductivity measureen_US
dc.titleLieb–Robinson Bounds for Multi–Commutators and Applications to Response Theoryen_US
dc.journal.titleSpringer Briefs in Math. Phys.en_US

Files in this item


This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España