Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory

J.-B. Bru

ISBN 10: 3319457837 / ISBN 13: 9783319457833

Published by Berlin Springer International Publishing Springer Dez 2016, 2016

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 109 pp. Englisch.

Seller Inventory # 9783319457833

Bibliographic Details

• Title: Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory
• Publisher: Berlin Springer International Publishing Springer Dez 2016
• Publication Date: 2016
• Language: English
• ISBN 10: 3319457837
• ISBN 13: 9783319457833
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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 mathematicswith 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.

Review

“This volume deals with Lieb-Robinson bounds for multi-commutators of fermionic systems. ... This book is reasonably self-contained ... and has complete proofs in the parts describing more recent developments of the theory (Chapters 4– 6). It is recommended for researchers wanting to learn about generalization of Lieb-Robinson bounds and some of its important applications in the description of quantum matter.” (Fernando Lledó, zbMATH 1379.81047, 2018)