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

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Science, Physics, Mathematical Physics
Cover of the book Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory by J.-B. Bru, W. de Siqueira Pedra, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: J.-B. Bru, W. de Siqueira Pedra ISBN: 9783319457840
Publisher: Springer International Publishing Publication: November 30, 2016
Imprint: Springer Language: English
Author: J.-B. Bru, W. de Siqueira Pedra
ISBN: 9783319457840
Publisher: Springer International Publishing
Publication: November 30, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Testing and Validation of Computer Simulation Models by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Racing the Moon’s Shadow with Concorde 001 by J.-B. Bru, W. de Siqueira Pedra
Cover of the book The Perioperative Medicine Consult Handbook by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Teaching and Learning of Energy in K – 12 Education by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Geological Core Analysis by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Nature, Tourism and Ethnicity as Drivers of (De)Marginalization by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Challenges and Opportunities for Agricultural Intensification of the Humid Highland Systems of Sub-Saharan Africa by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Rabindranath Tagore by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Continuous and Distributed Systems II by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Global Mobile Satellite Communications Theory by J.-B. Bru, W. de Siqueira Pedra
Cover of the book The Brazilian Microbiome by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Past and Present Interactions in Legal Reasoning and Logic by J.-B. Bru, W. de Siqueira Pedra
Cover of the book A Journey Around the Different Scales Involved in the Description of Matter and Complex Systems by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Corneal Collagen Cross Linking by J.-B. Bru, W. de Siqueira Pedra
Cover of the book Power Switching Components by J.-B. Bru, W. de Siqueira Pedra
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy