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

J.-B. Bru, W. de Siqueira Pedra (Autoren)

Buch | Softcover

VII, 109 Seiten

2016 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-45783-3 (ISBN)

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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.

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.

"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)

“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)

Erscheinungsdatum	06.01.2017
Reihe/Serie	SpringerBriefs in Mathematical Physics
Zusatzinfo	VII, 109 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	AC-conductivity measure • Condensed matter physics • Constructive QFT • Constructive Quantum Field Theory • Fermion Fock spaces • Functional Analysis • Functional analysis and transforms • Interacting fermions • Lattice Fermi • materials / states of matter • Mathematical methods in physics • Mathematical Physics • Minimally connected graph • Paramagnetic conductivity • Perturbed autonomous dynamics • Physics and Astronomy • Quantum Information Technology, Spintronics • Quantum physics (quantum mechanics and quantum fie • Quantum spins on lattices • Quantum Spin Systems • Representation Theory
ISBN-10	3-319-45783-7 / 3319457837
ISBN-13	978-3-319-45783-3 / 9783319457833
Zustand	Neuware