A Computational Non Commutative Geometry Program For Disordered Topological Insulators

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A Computational Non-commutative Geometry Program for Disordered Topological Insulators

Author : Emil Prodan
Publisher : Springer
ISBN 13 : 3319550233
Total Pages : 118 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis A Computational Non-commutative Geometry Program for Disordered Topological Insulators by : Emil Prodan

Download or read book A Computational Non-commutative Geometry Program for Disordered Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2017-03-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cyclic Cohomology at 40: Achievements and Future Prospects

Author : A. Connes
Publisher : American Mathematical Society
ISBN 13 : 1470469774
Total Pages : 592 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Cyclic Cohomology at 40: Achievements and Future Prospects by : A. Connes

Download or read book Cyclic Cohomology at 40: Achievements and Future Prospects written by A. Connes and published by American Mathematical Society. This book was released on 2023-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.

Geometric Methods in Physics XXXVIII

Author : Piotr Kielanowski
Publisher : Springer Nature
ISBN 13 : 3030533050
Total Pages : 373 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2020-10-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Bulk and Boundary Invariants for Complex Topological Insulators

Author : Emil Prodan
Publisher : Springer
ISBN 13 : 3319293516
Total Pages : 204 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Bulk and Boundary Invariants for Complex Topological Insulators by : Emil Prodan

Download or read book Bulk and Boundary Invariants for Complex Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2016-02-05 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-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.

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

Author : Hermann Schulz-Baldes
Publisher : Springer Nature
ISBN 13 : 3031122011
Total Pages : 225 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems by : Hermann Schulz-Baldes

Download or read book Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems written by Hermann Schulz-Baldes and published by Springer Nature. This book was released on 2022-12-31 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.

The Role of Topology in Materials

Author : Sanju Gupta
Publisher : Springer
ISBN 13 : 3319765965
Total Pages : 297 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Role of Topology in Materials by : Sanju Gupta

Download or read book The Role of Topology in Materials written by Sanju Gupta and published by Springer. This book was released on 2018-04-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

Non-commutative Geometry in Mathematics and Physics

Author : Giuseppe Dito
Publisher : American Mathematical Soc.
ISBN 13 : 9780821857908
Total Pages : 156 pages
Book Rating : 4.8/5 (579 download)

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Book Synopsis Non-commutative Geometry in Mathematics and Physics by : Giuseppe Dito

Download or read book Non-commutative Geometry in Mathematics and Physics written by Giuseppe Dito and published by American Mathematical Soc.. This book was released on 2008 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics.

Condensed Matter Field Theory

Author : Alexander Altland
Publisher : Cambridge University Press
ISBN 13 : 0521769752
Total Pages : 785 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Condensed Matter Field Theory by : Alexander Altland

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators

Author : Heejae Kim
Publisher : Springer Nature
ISBN 13 : 9811690774
Total Pages : 171 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators by : Heejae Kim

Download or read book Glide-Symmetric Z2 Magnetic Topological Crystalline Insulators written by Heejae Kim and published by Springer Nature. This book was released on 2022-01-25 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive theory on glide-symmetric topological crystalline insulators. Beginning with developing a theory of topological phase transitions between a topological and trivial phase, it derives a formula for topological invariance in a glide-symmetric topological phase when inversion symmetry is added into a system. It also shows that the addition of inversion symmetry drastically simplifies the formula, providing insights into this topological phase, and proposes potential implementations. Lastly, based on the above results, the author establishes a way to design topological photonic crystals. Allowing readers to gain a comprehensive understanding of the glide-symmetric topological crystalline insulators, the book offers a way to produce such a topological phase in various physical systems, such as electronic and photonic systems, in the future.

Geometric Methods in Physics XXXVIII

Author : Piotr Kielanowski
Publisher : Birkhäuser
ISBN 13 : 9783030533076
Total Pages : 381 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2021-10-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Algebra, Geometry, and Physics in the 21st Century

Author : Denis Auroux
Publisher : Birkhäuser
ISBN 13 : 3319599399
Total Pages : 364 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Algebra, Geometry, and Physics in the 21st Century by : Denis Auroux

Download or read book Algebra, Geometry, and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Advances in Noncommutative Geometry

Author : Ali Chamseddine
Publisher : Springer Nature
ISBN 13 : 3030295974
Total Pages : 753 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine

Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Statistical Mechanics

Author : James Sethna
Publisher : OUP Oxford
ISBN 13 : 0191566217
Total Pages : 374 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Statistical Mechanics by : James Sethna

Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

Introduction to Stochastic Analysis

Author : Vigirdas Mackevicius
Publisher : John Wiley & Sons
ISBN 13 : 1118603249
Total Pages : 220 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Introduction to Stochastic Analysis by : Vigirdas Mackevicius

Download or read book Introduction to Stochastic Analysis written by Vigirdas Mackevicius and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.

The Mathematics and Topology of Fullerenes

Author : Franco Cataldo
Publisher : Springer Science & Business Media
ISBN 13 : 9400702213
Total Pages : 294 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis The Mathematics and Topology of Fullerenes by : Franco Cataldo

Download or read book The Mathematics and Topology of Fullerenes written by Franco Cataldo and published by Springer Science & Business Media. This book was released on 2011-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.

An Introduction to K-Theory for C*-Algebras

Author : M. Rørdam
Publisher : Cambridge University Press
ISBN 13 : 9780521789448
Total Pages : 260 pages
Book Rating : 4.7/5 (894 download)

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Book Synopsis An Introduction to K-Theory for C*-Algebras by : M. Rørdam

Download or read book An Introduction to K-Theory for C*-Algebras written by M. Rørdam and published by Cambridge University Press. This book was released on 2000-07-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

A Short Course on Topological Insulators

Author : János K. Asbóth
Publisher : Springer
ISBN 13 : 3319256076
Total Pages : 166 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis A Short Course on Topological Insulators by : János K. Asbóth

Download or read book A Short Course on Topological Insulators written by János K. Asbóth and published by Springer. This book was released on 2016-02-22 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.