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Sinopsis
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields.
The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivialinvariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators.
This book is intended for advanced students in mathematical physics and researchers alike.
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Hermann Schulz-Baldes has been professor at the Department of Mathematics of the University of Erlangen since 2004. Before this he received his PhD from the University of Toulouse under the supervision of Jean Bellissard, and he held several positions at TU Berlin and University of California at Irvine. His research focuses on the quantum Hall effect, quantum transport, and topological insulators.
Emil Prodan is full professor of physics at the Yeshiva University. Before this he received his PhD from the Rice University under the supervision of Peter Nordlander, and he has held several positions at University of California Santa Barbara and Princeton University. His research combines rigorous mathematical and computer simulations to study the physics of the condensed matter. He received the NSF CAREER award to support research on topological insulator.
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This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields.
The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.
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Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)
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Bulk and Boundary Invariants for Complex Topological Insulators (Paperback)
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Springer International Publishing AG, Cham, 2018
ISBN 10: 3319805509
ISBN 13: 9783319805504
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Paperback. Condición: new. Paperback. This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields.The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivialinvariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike. This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9783319805504
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Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)
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Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)
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Bulk and Boundary Invariants for Complex Topological Insulators
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Springer International Publishing Mrz 2018, 2018
ISBN 10: 3319805509
ISBN 13: 9783319805504
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields.The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivialinvariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators.This book is intended for advanced students in mathematical physics and researchers alike. 228 pp. Englisch. Nº de ref. del artículo: 9783319805504
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Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)
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Bulk and Boundary Invariants for Complex Topological Insulators
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ISBN 10: 3319805509
ISBN 13: 9783319805504
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Offers a complete and detailed description of the state of theart in the field from a mathematics point of viewContains many original contributions such as the generalized Streda formula, the ranges of the pairings of K-th. Nº de ref. del artículo: 448755627
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Bulk and Boundary Invariants for Complex Topological Insulators
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Springer International Publishing, Springer Nature Switzerland Mär 2018, 2018
ISBN 10: 3319805509
ISBN 13: 9783319805504
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Librería: buchversandmimpf2000, Emtmannsberg, BAYE, Alemania
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Taschenbuch. Condición: Neu. Neuware -This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields.The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivialinvariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators.This book is intended for advanced students in mathematical physics and researchers alike.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 228 pp. Englisch. Nº de ref. del artículo: 9783319805504
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