Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory (Paperback, 1st ed. 2017)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	SpringerBriefs in Mathematical Physics, 13
Release date:	December 2016
First published:	2017
Authors:	J -B Bru • W. de Siqueira Pedra
Dimensions:	235 x 155 x 6mm (L x W x T)
Format:	Paperback
Pages:	109
Edition:	1st ed. 2017
ISBN-13:	978-3-319-45783-3
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > States of matter > General Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN:	3-319-45783-7
Barcode:	9783319457833

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