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Lieb-Robinson bounds for multi-commutators and applications to response theory

Author: J -B Bru; W De Siqueira Pedra
Publisher: Cham, Switzerland : Springer, 2017. ©2017
Series: SpringerBriefs in mathematical physics, v. 13.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bru, Jean-Bernard.
Lieb-Robinson bounds for multi-commutators and applications to response theory.
Cham, Switzerland : Springer, ©2017
(OCoLC)954425781
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J -B Bru; W De Siqueira Pedra
ISBN: 9783319457840 3319457845
OCLC Number: 967393021
Description: 1 online resource (113 pages).
Contents: 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.
Series Title: SpringerBriefs in mathematical physics, v. 13.
Responsibility: J.-B. Bru, W. de Siqueira Pedra.

Abstract:

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.

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"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 Read more...

 
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