Download E-books Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies) PDF

This monograph bargains an outline of rigorous effects on fermionic topological insulators from the advanced periods, particularly, these with no symmetries or with only a chiral symmetry. specific concentration is at the balance of the topological invariants within the presence of sturdy sickness, at the interaction among the majority and boundary invariants and on their dependence on magnetic fields.

The first half provides motivating examples and the conjectures recommend by means of the physics group, including a quick evaluate of the experimental achievements. the second one half develops an operator algebraic strategy for the learn of disordered topological insulators. This leads clearly to using analytical instruments from K-theory and non-commutative geometry, resembling cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New effects comprise a generalized Streda formulation and an explanation of the delocalized nature of floor states in topological insulators with non-trivial invariants. The concluding bankruptcy connects the invariants to measurable amounts and therefore provides a elegant actual characterization of the complicated topological insulators. 

This ebook is meant for complicated scholars in mathematical physics and researchers alike.

Show description

Read or Download Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies) PDF

Similar Abstract books

Introduction to Local Spectral Theory

Glossy neighborhood spectral thought is outfitted at the classical spectral theorem, a primary lead to single-operator idea and Hilbert areas. This booklet presents an in-depth creation to the normal growth of this attention-grabbing subject of Banach area operator conception. It provides whole assurance of the sector, together with the elemental contemporary paintings through Albrecht and Eschmeier which gives the total duality idea for Banach area operators.

More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics)

With company foundations relationship merely from the Nineteen Fifties, algebraic topology is a comparatively younger quarter of arithmetic. There are only a few textbooks that deal with basic themes past a primary direction, and lots of subject matters now necessary to the sector usually are not taken care of in any textbook. J. Peter May’s A Concise path in Algebraic Topology addresses the traditional first direction fabric, similar to primary teams, protecting areas, the fundamentals of homotopy conception, and homology and cohomology.

Lie Groups: An Approach through Invariants and Representations (Universitext)

Lie teams has been an expanding zone of concentration and wealthy examine because the heart of the twentieth century. In Lie teams: An technique via Invariants and Representations, the author's masterful technique offers the reader a accomplished therapy of the classical Lie groups besides an in depth advent to quite a lot of issues linked to Lie teams: symmetric capabilities, conception of algebraic types, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic teams, team representations, invariants, Hilbert thought, and binary kinds with fields starting from natural algebra to sensible research.

Topological Methods in Group Theory (Graduate Texts in Mathematics)

This ebook is set the interaction among algebraic topology and the speculation of endless discrete teams. it's a highly very important contribution to the sphere of topological and geometric team concept, and is sure to turn into a regular reference within the box. to maintain the size average and the focal point transparent, the writer assumes the reader is familiar with or can simply research the required algebra, yet desires to see the topology performed intimately.

Additional resources for Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics (Mathematical Physics Studies)

Show sample text content

Rated 4.82 of 5 – based on 6 votes