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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik A Computational Non-commutative Geometry Program for Disordered Topological Insulators
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A Computational Non-commutative Geometry Program for Disordered Topological Insulators
Emil Prodan (Taschenbuch, Englisch)
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Beschreibung
This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators,… where it facilitated many rigorous results concerning the stability of the topological invariants against disorder.In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation.The book is intended for graduate students and researchers in numerical and mathematical physics. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
23.03.2017
Sprache
Englisch
EAN
9783319550220
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
SpringerBriefs in Mathematical Physics
Sonderedition
Nein
Autor
Emil Prodan
Seitenanzahl
118
Einbandart
Taschenbuch
Schlagwörter
Bloch algebras, disordered topological insulators, homogenous disordered crystals, non-commutative Brillouin torus, Sobolev spaces, canonical finite-volume algorithm, non-commutative Kubo formula, integer quantum Hall effect, Chern insulators, Aizenman-Molchanov bound, Topological invariants
Thema-Inhalt
PHU - Mathematische Physik
PHFC - Physik der kondensierten Materie (Flüssigkeits- und Festkörperphysik)
PBPD - Algebraische Topologie
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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