1.

Record Nr.

UNINA9910155320803321

Autore

Bru J.-B

Titolo

Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory / / by J.-B. Bru, W. de Siqueira Pedra

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (VII, 109 p.)

Collana

SpringerBriefs in Mathematical Physics, , 2197-1757 ; ; 13

Disciplina

530.12

Soggetti

Physics

Mathematical physics

Functional analysis

Condensed matter

Quantum computers

Spintronics

Mathematical Methods in Physics

Mathematical Physics

Functional Analysis

Condensed Matter Physics

Quantum Information Technology, Spintronics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Introduction -- Algebraic Quantum Mechanics -- Algebraic Setting for Interacting Fermions on the Lattice -- Lieb–Robinson Bounds for Multi–Commutators -- Lieb–Robinson Bounds for Non–Autonomous Dynamics -- Applications to Conductivity Measures.

Sommario/riassunto

Lieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions. In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution



equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*-algebraic setting for lattice fermions, as well as the celebrated Lieb-Robinson bounds for commutators, are explained in detail, for completeness.