{"product_id":"9783319550220","title":"SpringerBriefs in Mathematical Physics","description":"\u003ch1\u003eSpringerBriefs in Mathematical Physics\u003c\/h1\u003e \u003ch2\u003eProdan, Emil\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThis 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.\u003c\/div\u003e\u003cdiv\u003eIn 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. \u003c\/div\u003e\u003cdiv\u003eIn 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. \u003c\/div\u003e\u003cdiv\u003eIn 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.\u003c\/div\u003e\u003cdiv\u003eThe book is intended for graduate students and researchers in numerical and mathematical physics.\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-03-23\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319550220\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-55023-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 118\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":47409991090316,"sku":"9783319550220","price":53.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319550220.jpg?v=1775835693","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319550220","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}